Polish
Jam...if you have a Dremel, take it over to a construction site and let a dump truck run over it a few times...then come back to your pistol. At any rate, try cleaning the extractor and its tunnel first. Easy to remove. Just use a nail or other suitable tool to push in on the firing pin. Slide the firing pin stop plate down until it's almost clear amd place your thumb over the firing pin to keep it from bouncin' off the wall. Don't point it at your face!
Ease the firing pin out and use the nail to pry the extractor out. There's a slot on the inner wall that'll work. When you put it back together, slip it in and use the firing pin stop plate to align it. Inser the firing pin and spring and push it in far enough to slide the firing pin stop plate into place. The firing pin will pop out through the hole in the plate when it's right. If you take the spring off the firing pin, remember that it goes on one way. If it falls off, turn it around. it's supposed to be a press-fit onto the pin.
Again...Careful of your eyes. Point it away from your face. Better to lose the firing pin for a few minutes than go down the highway of no return.
Use 600-grit paper on your fingertip to polish the ramp and throat. Do NOT round off the corner at the top of the frame's feed ramp. You may round off the corner at the top of the barrel throat a little.
Nicky...No reason that the gun shouldn't feed Lawman ammo if things are squared away. If you're within driving distance of Lexington, NC, bring it by and we'll take care of it, N/C.
Fuff...Since it's a Thompson AO, you're probably right about that cast extractor. Hopefully, somebody has swapped it for a decent one by now...