Not to drag this on too long, but while I was in favour of a 3"/76.2mm gun, I think Allans approach is perfectly valid. Vickers are designing a gun which is good enough now (in fact probably better than the M2/M3 at this point?) which will be a better AP gun than those already available and with a substantially better HE capability. And I still think that with an improved charge and with shells following the APC-APCBC-APCR-APDS route, probably enough to see out the war.I've been consistently trying not to 'wank' the British, trying to make changes that without all the panics might have happened within a different timeframe. When the Grant's 75mm appeared in the Middle East, all of a sudden the cry was for dual purpose, but before that it was 6-pdrs at all costs because the 2-pdr was struggling against the German face-hardened armour. Here the need for a dual purpose purpose is a bit ahead of time, as is the 6-pdr. The follow on, which OTL becomes the Vickers 77mm HV started life as a 75mm. I'm trying to work within the situation that I imagine that Cardin et al are working from. Yes, in retrospect would the 3-inch, 76.2mm gun have been the better choice, probably, but from my point of view, do we really have to make all the right decisions all the time?
The French were using the 75mm on the Char B1, the short 75mm on the captured Pz IV gave some clues about ammo types, and the Americans have gone with a 75mm on the Lee/Grant. While it isn't a common British gun, it is a gun that Vickers have experience of, and is not currently being used for anything else. Will the OTL change make it become the 77mm HV? That is entirely possible, but at this point the Pz III and IV need the 6-pdr, which the Valiant II will give. By 1943-44, the arrival of the Pz V and VI will make the British think about something more powerful, but the current 75mm HV does what Carden wants. It gives better penetration than the 6-pdr and has a good HE, which without the benefit of hindsight, seems a reasonable route to take.
I do wonder whether this might encourage the US Army to follow a similar path for their 75mm gun - see this -
Sherman Tank Myths - Hyper-Shot (HVAP or APDS) Was Not Feasible For The 75-mm On The Sherman | PDF | Shell (Projectile) | Anti Tank Warfare
Sherman Tank Myths - Hyper-Shot (HVAP or APDS) Was Not Feasible for the 75-mm on the Sherman. In reality, the US Army developed it but then did not issue it.