RL;CC
I have an Auto Ordnance TM1 made by Numrich West Hurley NY (not the later Auto Ordnance Kahr Arms) that I bought used.
TM1 is their WWII M1A1 replica with semi-auto only and 16.5 inch barrel, opposed to original select fire and 10.5 inch barrel. Since the M1 was designed after the military dropped the Tyle L (50) drum for the Type XXX (30) stick magazine, the M1 accepts only the Type XXX sticks. Some of the original Type XX (20) sticks have thicker back ribs than the GI Type XXX and may be a tight fit on an M1 or TM1.
Sights
Rear sight is a ∩ shape with a generous peep hole for 50-100 yards and a notch at the top for 200 yards. I drilled a smaller hole in a piece black Dymo label tape and zeroed mine for 100 yards with Win White Box .45 ACP. Grouped about six inches at 100 yards.
Cocking
It's a .45 ACP closed-bolt semi-auto. Means heavy bolt and heavy springs. Much harder to cock than a full-auto open-bolt Thompson that fires as the bolt is still moving forward. I cut, fit and glued a section of drumstick to fit inside the TM1 side-cocking handle to extend the handle by 3/4 inch and give me more grip on the handle to cock the bolt.
Accuracy
I shot mine in the military match at the local gun club in 2011 because I had a lot of 45 ACP but was short on .30 Carbine and 7.62x39mm. Standing position, standard bullseye target at 100 yards, ten shots each target, perfect score 100, my best target was 82. The worse targets got taped over and used up in later practice or sight-ins, so I don't recall what they were.
The gun could shoot 85 to 95 all day but the weight could be tiring.
"Besides, it weighs a ton!"
My TM1 weighs 12 pounds with a loaded twenty shot Type XX stick. My M70AB2 Yugo Kalashnikov weighs 10 pounds with a loaded thirty shot magazine, and my M1 Carbine with side magazine pouch and two loaded 15 shot magazines weighs a bit over 7 pounds. They do make an aluminum trigger frame and receiver version that weighs 8 pounds. I am told the aluminum trigger frame alone cuts 2 pounds from the weight (since the upper receiver carries the serial number, the trigger frame is just a part).
"The mags that come with the gun are simply refinished surplus with the magazine catch locking hole filed upward to allow the semi-auto mag catch to engage. If the mag is worn or if the hole was not fitted correctly and allows the mag to ride too low, reliability can be poor."
The magazine that came with my used gun did not fit well or feed reliably (might be why I got a good price). I already had a couple of GI surplus Type XXX sticks, and carefully cut those myself to fit well. It has been as reliable as my AK and M1 Carbine. At the time, GI surplus Thompson mags were $15 and magazines for the AO semi-auto were $55. Some folks report replacing the semi-auto magazine catch with an original magazine catch to allow use of unaltered GI magazines.
Numrich and Kahr specified the Semi-auto Thompson was designed for brass cased ammo, 230 grain FMJ ammo, standard .45 ACP pressure. Imagine Mommy Dearest (or Basic Training Instructor whoever's scarier) telling you: NO. Steel. Cased. Ammo. Ever!! I tried a type of aluminum cased .45ACP shotshell that had worked fine in my .45 pistol, and got a bad jam that broke the extractor year one. Ordered a replacement extractor and has worked fine ever since with brass cased, 230RN FMJ, standard velocity only.
With the lower frame with buttstock (18 inches) removed from the upper barreled receiver (29 inches), my TM1 fits a 31 inch violin case with foam lining cut out for the components and two Type XXX magazines. (Assembled length is 37.5" due to overlap.)
That's some of my notes on my Auto Ordnance Thompson, but your mileage may vary.
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* Internet code RL;CC real long post; get a cup of coffee. Otherwise TL;DR teal deer: too long; didn't read.