I am still overseas and can’t access my references, but the main differences between C and D are the engine deck and the hatch on the hull top. You could load the engine deck with stowage and a tarp to cover that, as an easy solution. accurate Armour did a replacement deck, or you could try and fill the incorrect hatch cover separation lines, remove hinges and handles, etc. The triangular hatch and hinge mods for a D would not be too hard to scratch build. There is a 3d file on Cults3D you can buy if you have access to a 3 D printer.
In regard the registration numbers, the ones to fit the Tamiya hull would be in the T189 and T190 ranges (hence the T187 in the kit are wrong markings for the type)
The F type had the side opening second hull hatch, and as this meant the stowage box as per earlier types had to be removed, additional boxes were added to the turret during construction.
If I recall correctly, the D type was the most numerous in active service, the F started to be issued in June 1944 - but do not quote me, as this is memory, not from checking my sources!
Also, Cromwell made by Vauxhall had a special one piece hatch.