Bigger hatches, little more power and speed, a duel purpose gun from the start and don't rush it into service before all the needed testing and development work is done. It wasn't ready when it entered service, the factory knew it, the army knew it and the crews got the idea when they saw the manual had a large number of blank pages for them to write down how they fixed the bugs.
The A22 Churchill was merely Vauxhall's successor to the Harland & Wolff's A20 infantry tank, which itself was originally a turretless tank with sponson armament converted to have a simplified version of the Matilda II's turret. Since neither company was experienced with tank building and Vauxhall was mostly improving on H&W's design, the Churchill kept archaic design features such as the envelopping tracks on a double girder hull, and a narrow fighting compartment and turret ring diameter (limited by the need to use Matilda II's turret).
Naturally by the time the Tank Board was formed in mid-1940 and was looking over the design, France had fallen and the British wanted new tanks ASAP, so while some like Pope wanted to start from scratch and others like Stern went on to design the TOG tanks (tbh the engineers in charge of the TOG did a really good job, making a tank that was easy and cheap to produce and had impressive performance for the time, but the requirements were completely stupid), expediency and interference from the Prime Minister led to the A22 being pursued as is.
Thus while delaying production could have helped, especially to produce more cruiser tanks as the Tank Board desired (there was strong imbalance in production between either type), it was not possible in the pyschology of the time.
Arguably the British should have been able to design a proper replacement based on the Cromwell to replace the Churchill by 1943 as intended, but did a rather poor job at it while Vauxhall pushed hard to save its design and the Churchill eventually proved itself.
Similarly, some improvements to the Churchill didn't happen until the Churchill VII because of the need to not disrupt production, because it was thought this tank would be replaced quickly enough, and because only a major redesign could justify those changes. This is why the welded hulls designed by Babcock & Wilcox, built in the end of 1940 and ballistically tested by mid-1942, were not introduced until 1944. So IMO the plausible way to go requires two approaches to be explored at the same time (and ideally, cancell the TOG earlier to have the SVDC work with Vauxhall): improvements that can be quickly integrated in current production, and a complete redesign to enter service by 1943 or 1944.
Current production options:
- have Leyland continue development of its diesel engine beyond December 1942 when trials ended. (possible introduction in mid-late 1943)
- based on early testing showing how it was impossible to use the gun on the move in 1941, have future turrets (for Mk IV and later in particular) featured geared elevation mechanisms and an external mantlet to increase room in the turret and possibly gun depression (supposedly it shouldn't interfered with hull crew hatches because the NA 75 conversions with Sherman mantlets worked). The external mantlet would also remove tendency of the internal version to be jammed by small arms fire and might allow an extended bustle to balance and get further space, but this must be limited in weight growth because the turret ring won't handle it.
- based on early 1942 trials in North Africa, introduce armored ammunition bins (4mm thick if armor steel, 6mm if mild steel) to reduce the chance of ammunition fires due to spall hitting them. Even if that means less ammo carried.
- based on the same trials, future turret mounts should have the BESA moved to the right side and improve the sights for long-range shooting
- turret style could be modernized to the level of the Vauxhall Cromwell's proposal (that was in late 42 IIRC) with external mantlet
For a longer-term redesign (kind of a mix between the BP and Churchill VII) on top of VII improvements:
- have the front idlers moved down like on the Black Prince to improve the driver's vision
- get rid of the stepped front hull design to incorporate 45-55° sloped armor. Ideally the angle would be set to increase the length of the roof, allowing for larger crew hatches or clearance for an external mantlet. This would allow to match or even exceed the level of protection of the Churchill VII, with reduced weight, reduced plate thickness (simplifying production or improving plate quality) and increased internal volume. This would also allow the removal of the weakpoints the MG mount and driver's viewport represented. This might not be compatible with a hull BESA MG, in which case the hull gunner can be removed to make place for a revised ammunition stowage.
- redesign the engine bay to use the RR Meteor if allowed.
(This was actually suggested in about October 1943 for BP, but obviously too late to matter. The MG was to be sacrificed if it could not be used)
- increase size as necessary to either: match the Cromwell's 60" turret ring diameter and standardize turrets while increasing space OR get all the way to BP or Comet-sized turrets, or something inbetween to use either the 17 pounder or 77mm gun.
I agree with an engine and hatch upgrades as improvements but I would go with the 77mm not the 17 per. It is almost as good and is much smaller.
Indeed, it would allow for a lighter and smaller design than the BP.