John,
Unless you are getting a class 3 weapon, you DO NOT need a signoff from anyone, tax stamp or to pay any funds.
You said above that you are interested in buying a semi-auto rifle, and all you need to do is to go to a gunshop, fill out the paper and pay for the weapon. Believe that there may be a small fee for the BS ATF background check but thats it.
Kinda confused on what you are looking for. The M1A is a semi-automatic rifle with a 20" or longer barrel, its not made with a 10" barrel nor would anyone want to fire this weapon with a cut down barrel. Recoil would be unbelieveable and noise would be worse. Accuracy would be terrible.
"Thompson" can be either Thompson Center, or a copy of the Thompson submachine gun. The Thompson Center contender makes a single shot pistol in just about every caliber made in the world and various rifles, usually bolt action.
Auto Ordinance/Kahr makes copies of the old Thompson submachine gun that are semi auto and have a 16.5 inch barrel that you mentioned. These are the M1, M1C, and so on. Is this the one you are talking about? They as well list full auto weapons but they are "not in production" at this time and for law enforcement only as well. None of these being sold now are full auto and do not require anything special of the ATF. Possibly by your home state or city authorities but otherwise not.
http://www.auto-ordnance.com/ao_front_lg.html
Hope this helps.
Joe A