Why would they know any more than they already do? Criminal records are public record.
If they actually do follow the law though, all that info is deleted shortly after the check is complete. The only record should be the 4473 the FFL keeps.
or we can push for a more intelligent system similar to what has been mentioned earlier with a notification on the drivers license/ID.
So you say. Do you have proof that there isn't any record keeping done by the NICS or FBI that's currently in place, and that there is no "tally" kept on transfers done by, say, social security number? That's something you are required to use every time a transfer is done in your name, proof positive that you've bought another gun.
Such the same when a bad guy commits a crime and is processed, the ever-present social security number pops up. Crimes as you stated and most intelligent folk already are aware of, are public record.
I don't think convicted felons should be blanketed under any amendment, so I think a bimonthly updated license renewal (which is driver inclusive) that labels lawful or unlawful people as "Non Saleable" or "Saleable" is not an infringement on felons' rights, as they really have very little to begin with. If a person who is allowed to buy commits a crime of any nature above misdemeanor, revocation and renewal under "Non Saleable"
When doing a FTF, check the license of the buyer they can check yours, if its GTG, sell the gun. If the buyer is not a desirable, no sale and report the person trying to buy illegally.
This makes sellers happy and legal.
Keeps some guns out of some bad guys' hands.
The Fed gets to do a bimonthly background check by way of Department of Revenue.
We get to do things ourselves, and we keep some semblance of privacy.