Wow, you just brought back bad memories of having to sell some guns. I had to sell one three years ago while unemployed, though come to think of it I think I kept a whole bunch of the mags that I used with it (still hoping to someday buy a Thompson).
Bottom line is you just have to use semi-auto Thompson mags. These have an oval shaped hole on the back instead of a round one. Actually, I think I once bought a bunch of the full auto ones with the round hole and all I had to do was file the top of the hole to make it a bit more elongated and then they worked perfectly after that. The gun.....well, that's a different story. It was always very reliable, and fairly accurate, but the cheap construction always bothered me and the grip left a lot to be desired. I was also never able to field strip it as it was stuck together so hard I was afraid of breaking it taking it apart so I always just cleaned the barrel, then cleaned out the body by spraying it with break cleaner until it came out clean, then I sprayed BreakFree CLP into it using the little hose. It never failed to fire though.
For those of you not familiar, the way this rifle is built is basically like they took the receiver from those bb machine guns from the fair and made it into an actual firearm. I bought mine really cheap from a local gun shop that was known for being overpriced. Everyone familiar with the shop told me that if I'd bought it for that little, someone must have paid them to take it.
If you do try to do the modification yourself, just disassemble the mags and stick the body in, then file a little at a time, re-inserting it repeatedly as you go along. Once you have it just barely locking into place when you push it in hard, file a little more to make it reliable, then clean it up and re-assemble the mags. It's really not that hard.
BTW, I did manage to get a hold of an original manual once and scanned it so if you want a copy, I can send it to you. Just PM me.