I asked a couple of squaddies to help me with testing the HE rounds in the TA. What we found is what I expected.
The Tiger tanks have the strongest HE of course. The Firefly though has the same HE as the M4A3-75 which should not be. Even if you accept that the Firefly ammunition eventually had capable HE during the war (I do not) it should not match the M4A3 ammo (HE-APC). Also the HE-APC and AP-APC ammunition should both be much more similar in trajectory unless of course the round is AP-solid which we should not since the APC ammunition is more common in American and Britsh tanks (even the Churchill used APC). The HE ammunition in this case was 1.5 lbs of explosive compound and four ounces of fuse cap and fuse.
The fuse of the HE ammunition could be set in two ways. It would either go off on impact (right-away fusing) or delay in which case it could be varied. If variable fusing is granted I wish we could set it before launch and not while in the field.
During the breakout at Normandy the 75mm gun was found to be inadequate for the job against Panthers and Tigers. So they upsized the guns to 76mm and the 17lber for the Firefly (this is the short history version). They quickly discovered that the HE in those tanks was inferior to the M4A3 75mm HE-APC and so they stopped loading the HE rounds in the British tanks. Even though the Americans still had HE they would often prefer to load 100% AP since they knew the HE would do nothing for them. So in effect the British and American both only used HE in the M4A3 75mm and this is why the 75mm remained on the battlefield.
So this is a multi-faceted wish.
1) No HE in the Firefly
2) No HE in the M4A3-76
3) gunsite and trajectory correction of M4A3-75
4) Cruiser Tank Mk III Challenger
WRONG! I'm glad I get to beat Looshy in telling you so, too.

The Tiger II, Tiger, and T34/85mm all have the same HE damage: 234 lbs
Next in line is the US M4A3/75mm at 178 lbs.
Then a whole list of vehicles that deliver 156 lbs: Panther, Pzr IV's, LVT-4 (although it fires the SAME shell as the M4/75mm

), and T34/76.
Next in line is the British Firefly with 140lbs of damage.
Last in line for tank HE are the M4A3/76 and M18 at 103 lbs of damage.
Take a look at the scaling. It either takes 2, 3, or 4 shots to destroy a typical OBJ in AH (building, ord bunker, radar tower, etc). HTC has given the M4/75 a nod (and rightfully so) and upped its damage to make it worth more to hit hangers, etc, but on the scale it is still a 2 hit/OBJ to destroy. On a different note, the M4/75mm armed with the Calliope will far surpass what the Tiger offers in terms of HE destruction capability, and it can do it much faster thanks to an almost twice as fast reload.
I will agree that the Firefly could possibly have a reduced HE ammo load out. It was a designated tank destroyer, and unless there was an enemy tank to content with the Shermans and Cromwells and their superior 75mm HE did all the infantry support work. The M4A3/76mm is a different story though, it was ultimately designed to replace the M4A3/75mm, but by the time it arrived the upped 76mm gun was not as badly needed yet it served on. It did have a weaker HE round without a doubt. However, it still performed a direct support role right alongside the M4/75mm and the infantry. I say leave it alone.
I was not aware of an sun sight inaccuracy in the M4/75mm. I guess I will pay more attention next time.
Oh, and if you want to test weapons, etc, vs OBJ then may I suggest going offline. Using the TA to measure anything is a bit of a stretch because the damage model and hardness settings are not in line with the MA.
I have a couple of spreadsheets showing weapons damage and tank data I've offered up to people in a different thread. Anyone who wants them is more than welcome to PM me their email and I will gladly send them.