I read your post at work, got home and setup a QB along the lines of what you describe (500 pts, ME, played allies with a Sherman 75mm as main unit). I won it in 13 turns even with some dumb mistakes. My advice to you (besides the good advice above) would be to re-evaluate how you move units.
Even when operating offensively, trying to gain territory or a VL, I find it helps to think defensively. Think "moving ambush". Infantry should be your eyes, move the heavy stuff (or unhide it as the case may be for AT guns) into position only when you can guess what they will run into and that most likely they will kill/disable the target.
Also, try to limit the LOS of your attacking units to only the target you plan to take out
in order to protect them from side shots.
I apologize if this advice is a little basic (I'm no expert myself), but defensive/ambush type thinking seems to help a lot in CM. Probably in real-life war as well!
Elysian