The problem is, the LCW is an NFA weapon -a short barreled rifle (aka you need the permits, and some states will NOT issue them), where the charger is a pistol

Huh you say? Gets crazier - if the company that makes the LCW buys a charger and makes their pistol from it, it's just a pistol (unless that is a supressor)

The second you call the receiver a "rifle receiver" (and sell it as a 10-22) and you change the barrel to under 18", you've created a short barrelled rifle. But if you make the identical receiver, but call it a pistol receiver, it's a pistol