Hi Dave...
I am puzzled by your comment about federal law preventing registration.
A few years ago I had a couple weapons ripped off, needed to file police report, insurance claim and so on...
As I was traveling I simply called the retail outlet where I had purchased them a year or two prior and they were able to look up my serial numbers, etc.
To my understanding (I could be wrong) they used my background check records to do so...does that sound unlikely to you?
The records of the sale remain with the dealer. They can be access by law enforcement only for legitimate purposes, like a weapon recovered in a crime.
The records do not go to a centralized place. They are not computerized. They are not available to the gov’t to use as it sees fit.
On the other end of the phone, the information from the FBI background check is purged. No record is kept of the names being queried. No permanent records, no computerization, not access to gov’t agencies. Nothing exists after the check is complete.