You could cut the barrel of the length of the suppressor and then permanently attach the suppressor to the barrel making it again 16".
I would register the USC as a SBR and then cut the barrel to the UMP length with a thread for the suppressor.
Then you can install the suppressor when ever you like.
I have fiddled with it off and on for years. The main problem that is encountered is the system. The UMP/USC is a straight blowback system. When you impede the expansion and exit of the gas at the muzzle, you force it to try and escape through the breech. This has a big downside, as many folks who have put muzzle mount cans have found: less perceived and real sound reduction and lots of crap blown back at the user. Cans work better on other systems because there is almost always, at least briefly, a sealing of the breech end.
In an integral system you "cheat." You port the barrel just past the breech to help bleed off the rapidly expanding gas into the suppressor body. You also capture the rapid expansion of the report at the muzzle end of the same suppressor body and use a set of baffles (one piece, K, etc.) to further impede the expansion, create turbulence in the expansion to alter the sound and provide more surface area to dissipate heat. In a straight blowback, the rapid expansion is going to take the path of least resistance when it can and that results in a lot crud/sound headed out the breech. Try to compensate too much and you unbalance the system to the point where reliable cycling becomes an issue. So you wind up doing a lot of work for little payoff.
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