The registration form doesn't have to match the configuration of the gun. It just has to match the configuration of the gun, at the time it was built or transferred. What happens if you build or transfer an NFA gun and then you move to a new residence? Your address has changed, and the information on the form doesn't match anymore. Oh no! Except, it doesn't matter.
You could engrave a serial number (or anything else) on the barrel, but a serial number there doesn't matter for NFA purposes, legally speaking. The maker's info (name and location) and the gun's model and caliber can be either on the receiver or barrel, but the serial has to be on the receiver.
See 27 CFR 479.102 (a)(1) and (2).
You could always engrave multiple barrels.