UNLESS Kahr has changed barrel threads (unlikely, too much trouble for no gain) ALL models of Thompson guns have interchangeable barrels.
This means a 1921 or M1A1 barrel will fit the semi-auto models, and a 16" semi-auto barrel will fit a 1921.
The problem is in doing the re-barreling.
The barrels on the semi-auto guns are put on at the factory by Godzilla. They're TIGHT, and very difficult to remove.
Second problem is the fore end support bar.
This is a steel bar projecting from the front of the receiver underneath the barrel that the front grip mounts to.
This bar is held in by the barrel, and cannot be removed until the barrel is removed.
The problem is, this bar interferes with getting a good set up with the barreling vise. You have to grip the barrel in front of the bar, and this makes for a "springy" set up which makes breaking the barrel loose a problem.
Semi-auto barrels are a pain to work with for this reason, but SBR's are quite do-able if you have the equipment and knowledge to work with them.
Among other gunsmithing projects on the semi-autos are changing the fixed M1 type frame to accept a 1921/28 detachable butt stock, improving the trigger pull, and altering the cocking handle on the 1927 semi-auto to look like a 1921 actuator.