AfterLife, the Form 3 is for a tax-free transfer from one Class 3 dealer to another (and a few other cases). It is not a way an unregistered NFA firearm can be registered.
Hawg, I am not sure just turning in the barrels would satisfy BATFE; they usually consider the receiver the gun and would want the owner to abandon the gun, not just part of it. Besides, getting a set of legal barrels for an old Remington shotgun would be next to impossible, and the gun is not worth enough to even bother.
There are always folks who claim to have some special way to get illegal NFA weapons registered and made legal. Someone claims to know someone who knows someone who does it all the time and has no problem. I confess to skepticism and have an idea that bringing an illegal gun to the "someone" could be the wrong move.