I've seen a fellow using one of those .351's at a Wild Bunch match here in New England a couple of times. He was using a lead bullet and had a muzzle velocity to SASS stardards for "main match rifles" so yeah, low power loads work. Wish I could remember who it was that had the thing!
On another note, would those reproduction Sterlings that are on the market be okay? They are a pre 1950 design, and shoot the 9mm. I think they'd be a fun alternative to the Thompson.
Of course, even if they are okay, I can't buy one...