I'm a glutton for punishment, so I'll reply.
I've fired several BARs. They're not too uncommon to see at the firing range I use, and there's several companies making new semi-auto versions. I've never fired an StG (ammo is scarce since no one manufactures it), but I've had my hands on several deactivated ones (sob) and one live one. BARs *are* heavy - but think of it as running holding two full one-gallon milk jugs as opposed to one for the StG. You're still gonna be fast.
For German weapons, there's plenty of old and new data. Most of this stuff's still around. The Department of the Army's Handbook on the German Army (published 1945) gives a good description of every piece of gear the Germans used from the Me-262 to folding spoon/fork combos. For new info - try a gun show. You can get your hands on a lot of this stuff, even if just to see what it really looks/feels like. Their info on german firearms is basic, but detailed enough for something like you're trying.
The StG was considered an assault rifle - that does not mean it was anything near a success. It was constructed mostly from steel stampings, the receiver wall was too thin, and the gas tube crushed like foil if you weren't careful. Everything I've read says they were not considered safe for sustained full auto.
Final point on BAR vs. StG - ballistics between the two rounds (.30'06 vs. 7.92x33mm) are in fact different, but both rounds will kill somebody dead at ranges under 200 yards.
My point behind all of this, and my beef with your post, is that I object to "realism" taking precedence over balance. MoH is so grossly unrealistic to start with that it's an exercise in futility to make a serious effort at making it "real". I certainly appreciate someone's taking the time to do some research (and props to you for doing so) - but don't get carried away
Cheers,
Panzerman