Turn that thought process around. The goal is not to find out “who’s gun is this?”, it is to determine “who has guns?” Stroke of a pen, law of the land, BATFE goes to each manufacturer and says “turn over your transfer records or we shut you down and take those records”, and starts following the paper trail from there. Should they reach “dunno, sold it to some guy in a private sale”, they will NOT just go “oh, ok, guess that lead is closed”, they’ll move to some variation of “rubber hose cryptography”. ...oh, and if someone says “boating accident”, every cubic foot of their residence will be turned over to a depth of 10 feet.
Before they get anywhere close to upending more than a few homes, word will get out. Hell, some patriot employed by the fed.gov may even spill the beans before the first raids begin.
At either point, the searches will have certain, uh, costs - yeah, that’s the ticket, COSTS - attached to them. Some of those costs may need to be paid directly by higher level management (you know, the peons never have the authority to pay for stuff, they just do as they’re told).
Hey, here’s a great scene from movie about a somewhat similar set of circumstances: http://moviesonline.ca/TheFeed/index.php?id=300-laydownyourweapons
>every cubic foot of their residence will be turned over to a depth of 10 feet.<
Anyone foolish enough to deep cache on their own property deserves the burns that will come from it.