N-L-M

1. Of the available tanks, the BT-5 is, IMO, the only reasonable choice.
1.1. The T-28 cannot be reasonably made a real opponent to the Sherman and is rare, with a spares issue just waiting to happen.
1.2. The various French light tanks and T-26 are disasters on tracks, with no armor, no real option to improve armament, and very poor automotives (low power to weight and low speed suspension).
1.3. Of the guns available, only the 7.62 cm PaK 39(r) can reliably kill a Sherman with AP, and that is neither in service nor will the Germans willingly part with them or their ammo in large quantities; Also, the case is that of the PaK 40, which cannot fit into any of these turrets anyway. Therefore any Sherman killing must require HEAT or some other means of defeating the tank without getting through the armor directly.

2. Why the BT-5 is a good choice
2.1. Most of what made the BT-5 a poor tank IRL are "soft" factors which can be fixed fairly cheaply and quickly, if the goal isn't to go up against Shermans.
2.2. The BT-5 is uniquely suited to being weighted down, owing to the frankly ludicrously over-specced drivetrain.
2.3. The added weight of the BT-7 vs the -5 did not by any source I've found adversely affect reliability, and again as far as I can tell the suspension was not heavily modified.
2.4. For going up against light tanks, the 45mm is quite good and perhaps does not require replacement at all, for a low-end option.
2.5. The sheer number taken intact by the Germans, as well as the large number of spares salvageable from disabled ones, allows a large and capable fleet.

3. Proposed BT-5 upgrade:
3.1. Mobility:
This is in fact a bit of a downgrade, to cope with the increased weight to be mentioned later.
3.1.1. Increasing the preload of the springs by spacers in the spring wells, to retain ground clearance.
3.1.2. Installing volute bump stops on first and last road wheel stations to prevent over-stressing springs, at cost of some of the very generous travel.
3.1.3. Installing drive wheels with 5 rather than 6 drive nubs to raise final drive ratio  - prevents over-stressing drivetrain at the cost of reduced speed at all gears. Even at a 5:6 reduced speed, the BT-5 is silly fast.
3.1.4. Delete wheeled drive feature as irrelevant.
All in all, very easy to do, requires light welding work to install bump stops and requires fabricating new drive wheels - not hard at all. Should allow a weight of around 15T vs the original 12T or so. Ground pressure in Italian terrain is also not that big of an issue, and the BT-5 has silly low MMP ground pressure anyway thanks to the massive track pitch.

3.2 Firepower:
While the firepower of the BT-5 is downright good for a prewar light tank, by the year 1943 we have learned a thing or two about armored warfare and the mechanical means needed to support such warfare.
3.2.1 Weapons
3.2.1.1 Main gun options
Not one, but 2 main gun options are offered!
3.2.1.1.1 45mm. Simplest, quickest, economy option. Fully compatible with the augmentations mentioned later.
3.2.1.1.2 76mm M1936 field gun or French 75mm refit with a vertical semi-auto breech. These guns are not held at the center of gravity, but rather the trunnions are biased aft on the tube, leaving most of the gun outside the turret and leaving sufficient room to load the longer rounds. The extra weight and imbalance caused by putting a larger gun farther out in front of the turret are compensated by welding on an extra box to the rear end of the turret, for carrying extra ammunition (only accessible from the outside).
The gun is also fitted with a large spring equilibrator to ease the manual elevation and depression.
The 75/76mm is to be fitted to carry HEAT based on the German Hl.38C or WP rounds for use against enemy tanks, as well as straight HE for general purpose use.
The 76mm gun can elevate to +10 degrees or depress to -5 degrees.

3.2.1.2 mechanical ram/eject
Replacing the spent case basket behind and under the breech, a recoil cocked spring operated trapeze mechanism for ejecting spent cases out through a tube over the gun barrel and a flick rammer are added to the 45mm or 76mm gun. This mechanism, inspired by the auto feed of 37mm AA guns but much simpler (owing to not being clip fed nor fully automatic) allows a much more comfortable operation despite the relatively cramped turret. Likewise, it allows the crew reorganization mentioned later.
3.2.1.3 Roof MG +modes of operation
A 12.7mm (Breda-SAFAT or Browning) or 13.2mm (Hotchkiss) HMG is added to the roof on a centreline pintle mount. In addition, there is a linkage tying the elevation of the roof MG to that of the main gun, and pointing it straight forwards. The gun is intended to fire straight API-T ammunition, and to be fired by the gunner from his position, thus acting as a spotting MG for the main gun.
As a secondary mode, the linkage and trigger have a quick detach, and the commander can operate the gun from his cupola in an anti-ground or anti-air role. The straight API load will provide quite a deterrent to aircraft, and the ability to punch through armor only rated for rifle caliber ammunition.
3.2.1.4 HE/WP projectors
Inspired by the British smoke projectors on the Matilda tanks, and using captured rifles, projectors are fitted to the sides of the turret to carry both WP smoke grenades and HE hand grenades. These provide good close in protection against bazooka teams and instantaneous smoke screening ability if heavy enemy forces are encountered. These grenades, standard in use with the Italian infantry, are impact fuzed, and the tubes are designed such that they only arm after leaving the tube.
3.2.1.5 Main gun mechanical ready rack
Behind the main gun rammer and the loader, a gravity fed hopper for two kinds of ammunition is fitted. By pulling on the relevant handle, the gunner pulls a round into the ramming tray of the mechanical rammer, and then presses the release to ram it in. This system allows the gunner to function as the loader, without ever taking his eyes off the sights, for as long as the relevant ammo type remains available in the hopper. Expected load - 3-4 rounds per type for 76mm, 5-6 rounds per type for 45mm.
3.2.1.6 Coax
In both 45mm and 76mm variants, the 7.62 DT coax MG is retained.
3.2.2 Optics
A major factor in improving firepower is increasing the ability of the tanks crew to locate, identify, and engage enemies before they do the same. To that end, the following improvements have been made to the to the BT-5:

3.2.2.1 Cupola
A wide vision cupola of armored glass windows (with steel shutters) topped with a hatch equipped with an open-protected position is installed on the right side of the turret, allowing good all-around vision.
The cupola also supports the use of ranging binoculars, should such be available.
3.2.2.2 Periscopes
The panoramic periscope at the gunners position is retained, and another, scavenged from damaged captured vehicles (including T-26, as they use the same model), is installed on the right side.
Likewise, a periscope is added to the left edge of the roof to replace the deleted viewport in the turret side.
3.2.3 FCS
3.2.3.1 The functionality of an RMG and commander’s independent sight as previously mentioned.
3.2.3.2 power traverse
An electric power traverse motor is installed to aid the gunner in his duty. Owing to the small size of the turret, even with added armor, a small unit is sufficient, even one scavenged from destroyed T-34s. An override control handle is also provided on the right for the commander.
3.3 Survivability
The most objectionable part of the BT-5, as provided, is definitely the armor, which is only really sufficient against HMGs from the front at range and rifle caliber AP and frag elsewhere. Therefore, in order to increase the combat utility against an enemy more than willing to shoot back, a significant improvement in protection is desired.
In order to bring about this improvement at a minimum cost in weight, as the BT-5 cannot support very much, highly efficient armor must be used.
We do, however note that the common types of ammunition in use, fullbore AP and APC, do not function efficiently against highly sloped armor, nor against spaced armor. Therefore, the up-armor scheme focuses on both these elements in order to provide reasonable protection at reasonable weight. Spaced armor of this type would also effectively prevent 75mm HE from just wrecking the tank, as the inner skin would likely remain intact.
Likewise, there are reports of Bazooka rounds failing to fuze properly upon impact with highly sloped armor, and the spaced effect would prevent an improper detonation from wrecking the tank anyway.

3.3.1 Hull armor
3.3.1.1The front of the hull is 13mm thick and angled at 60 degrees. Adding a 20mm plate at the same angle, but spaced as far as the vision slit allows, allows protection against 37mm point blank (0 yd vs M51B1 APC), 57mm at combat ranges (600 yd vs M70 AP-T, 250 yd vs M86 APC-T), and 75mm at combat ranges (250 yd vs M61 APC-T), but no protection against 76mm guns is offered (effective penetrations up to 1750 yd).
3.3.1.2 The hull side is 15mm vertical. 15mm skirts along the sides of the hull provide protection against 37mm in a roughly 90 degree frontal arc, and against 57mm or 75mm in around a 60 degree arc (at the ranges listed above for the frontal armor), as well as .50 AP point blank to the side and heavy fragments from 5”-6” shells.
3.3.1.3 Turret ring armor is added to the roof of the hull too, and is overhung by the turret armor packages, to avoid forming a shot trap.
3.3.1.4 Hull floor, roof, and rear are not modified.
3.3.2 Turret armor
Much like the hull front armor along the frontal arc in a wedge-shape form 25mm thick at 60 degrees, with vertical 15mm plates along the flanks like the hull side. Owing to the turret flanks being “angled in” at 17.5 degrees from the centreline each, the protected arc for the turret is wider by 35 degrees (125 degrees vs 37mm, 95 degrees vs 57mm or 75mm).
3.3.3 Smoke projectors
The smoke projectors mentioned in the firepower section are controlled from within the vehicle and provide quick obscuration to protect the vehicle.

Overall weight of the armor package: 2.5 tons, leaving 0.5 tons for the armament upgrade while remaining within 3 tons.

3.4 Fightability
In addition to improving “paper stats”, some changes have been made to how the vehicle is arranged for actually being used.
3.4.1 Crew arrangement
As designed, the BT-5 gunner is also supposed to be the commander, while the other turret crewmember is the loader. By providing a semi-automatic loading system, whereby the gunner (on the left) can also be the loader (while ready rounds last) without detracting from his role as a gunner, the right side of the turret can be remodelled into a commander’s position, where he can focus on his job (plus acting as loader for the machine guns).
This change should greatly increase the efficiency of individual tanks as well as that of the entire unit.
3.4.2 Vision
As mentioned in the firepower section, the addition and reorganization of optics allows much better visibility out of the vehicle, improving situational awareness and therefore combat effectiveness.

3.4.3 Communications
3.4.3.1 The right side of the turret bustle is occupied by a radio for the commander’s use.
3.4.3.2 An infantry telephone is fitted at the right rear.
3.4.3.3 The port for signal flags was deleted in favour of a panoramic periscope. To compensate, the hatch in the new cupola has a similar hole for flags or signal flare pistols.

3.5 Other variants
Though a battle tank was requested, it is known that tanks function best when they do not operate alone. It is therefore advised that brigade or division sized combat units be formed, and for the sake of cohesion it’s best if they are all of equal mobility and ideally based on the same chassis. The following vehicles are recommended to also be converted from the same chassis. Many of them may be built on hulls without functioning turrets, thus expanding the pool of captured vehicles recoverable.
3.5.1 SPG
The inability of the BT-5 to kill Shermans or other medium-heavy tanks from the front with high velocity AP is not ideal, and it is recommended to fit a PaK 39(r) in a fixed low profile superstructure either facing forwards or aft like an Archer. Such an SPG would also be useful for blasting landing craft out of the water.
3.5.2 SPH
A highly mobile unit requires highly mobile artillery to support it. For this purpose, it is recommended to install recoil spades on the nose of the BT-5, reinforce the hull, and install either a 105mm Mle 1913 Schneider captured from the French, or an Italian 4”/35 naval gun. Both are already in service in substantial numbers. It is further recommended to fit them with direct fire sights and gunshields for use against landing ships and for emergency use as anti-tank guns, where they are capable of defeating the armor of medium-heavy tanks, should the need arise.
3.5.3 SPAA
In this option, the turret roof and mantlet are cut open and a medium caliber 37mm or 40mm AA gun is installed. This gun not only offers local defense against aircraft, but is also extremely effective against light armored vehicles, landing craft, and troops in the open.
3.5.4 command
The Italian Army does not possess any command assets which are sufficiently mobile, and so a command tank wherein the gun is removed (dummy welded on), map tables installed, and an extra radio installed in the bustle (where the ammo is in the battle tank). Coax and roof MGs are retained for self-defense.
3.5.5 ARV
Replace the turret with a small crane, install a couple earth spades, and a winch for recovering disabled vehicles.
3.5.6 APC
Tank desant can carry the bulk of the infantry into combat, but for assaulting well-defended positions, there is a clear requirement for a vehicle which can transport troops in high threat areas. As there is not much room inside a BT-5, a superstructure is built up around the fighting compartment, armored at least enough to stop .50 AP, ideally with the full armor of the battle tank. Rear superstructure door for dismounting over the engine deck, one MG in a ball mount in the front, roof hatches, one roof HMG with gunshield, and firing ports for personal weapons completes this variant.


4. Conclusions.
The above proposal allows for a robust, highly mobile, and capable reaction force to any amphibious landing, while not requiring much in the way of industry to accomplish – No large or complex parts need to be produced (no large ring bearings, no complex curves), and no parts of extreme precision are required either (flame cut plates are sufficient for most parts). This means the existing industrial base may be put to good use quickly, and brigade sized units could be made available very quickly (while captured vehicle stocks last).

Armor numbers taken from US BRL charts avaliable here.