Think you would find that the APCR round were never issued. Could not find out the main reason but CR rounds have poor long range penetration. The APCR were tested in 1942 (have not seen the Ian Hogg book which states October 1943), and the APDS rounds were first used June 1944 in NWE.
6pdr armed churchills were used in NWE (several good books on the Normandy battles have photos) but not very widely. Some units replaced one 75mm tank per troop (or kept one)with a 6 pdr tank because the 6 pdr had better penetration even with standard AP rounds. 6pdr tanks were used more widely in Italy. One knocked out a sunken Panther turret on the Gothic? Line.
All the photographs of Churchill NA 75s I have seen were modified Mk IVs. Churchills armed with British 75mm had a muzzle brake fitted so no mistake with a 6 pdr. The NA 75 did not have one but the Sherman mantle is a big give away.
Churchill Mk IVs, Vs and VIs were upgraded to Mk VII standard but I have never seen a 75mm in a Mk III turret (less of this Mark were made compared to the Mk IV and poss most were converted to ARV, AVRE or had a Mark IV turret fitted). If the original turret was retained it had the suffix LT after the mark number. Very easy to ID because of the square hull doors, driver vision flap and lots of welded on armour. Have seen a photo of a NA 75 so converted (hull only). The Marks ran from IX, X and XI.
Hope this has been of some use and is from memory only so sorry for any slip ups. If anyone would like the sources just ask.
I have always found BTS research on British weapons poor from when CMBO was released and the last two games have not been much better. CMBB had very few British tanks in anyway! With no in game editor they will never be fixed.
Rune, you said you found a mini game that allows APCR for churchills. Was this SPWAW because this will allow anyone to edit anything in the game.