Thru my personal experience I am not buying into that the M3A1 is problematic to control in firing.
I dont buy into it either. The M3 was the first SMG I fired, and I was 8 at the time. I was given a few minutes instruction, and allowed to fire a couple of single rounds, to get the feel of the gun down, then a couple of mags loaded with three rounds, and then it was full mags and big smiles. I never had any troubles keeping rounds on target, even right off.
From that point on, I was hooked, and have been lucky enough to get to shoot all sorts of cool stuff over the years.
What I am really amazed at is, how little instruction most people in the military were (are now?) given, if they were given any at all. 95% of former military people Ive known and/or let shoot my guns, seemed to have no idea as to how to shoot and control the guns. The usual complaints of control and rising up and off target, just show they had no training in how to shoot them properly. Its a simple technique, easily learned and used, and full mag dumps on target are very easy. Not that thats the correct use of the gun, but it shows that shooting them isnt difficult.
As far as SA versions of any of them, sure, they would probably be fun, and Im sure a lot of reenactors would like to see them avaialble, especially the WWII stuff, but to be close to "real", they'd still be in the NFA, as they are to "short" by rifle standards with the correct barrels, and working stocks, and would need to be "taxed" as a "short barreled rifle".