I assume this is a semi-auto Auto-Ord replica?
If so, be aware that you won't get the exact correct profile barrel for an authentic WWII M1 or M1A1 if you just cut the existing barrel down to the correct length. The barrel profile on the 16" barrel is different than that of the true SMG barrel. (Which I think is 11"? Off the top of my head I can't recall for sure).
The reason I know this is that re-enactors or shooters who want to more closely replicate the look of the WWII Thompson with the shorter barrel will instead remove and replace the 16" barrel with the correct profile original SMG barrel instead of cutting down the 16" tube.
That may not be a consideration for you in this build. Just thought I'd mention it if you weren't aware of it, just in case it matters.
Btw, nice build so far. I've got one planned for when I have the cash. Gonna go with a semi-auto and dummy shotgun to avoid the second tax stamp. (Just one for SBR). If I ever have enough free cash for a real Thompson SMG I'd do a build that will be more easily converted back and forth between stock GI gun and Pulse Rifle.
(And yeah, I know how expensive registered Thompsons are, even AO SMG's. I already own a registered Uzi and a Thompson is on my list if I can get enough together to buy a second SMG