Here's one I think EVERYONE (conservative and progressive) can agree on.

Gun ownership should be contingent upon doing one's duty as a US citizen.

Therefore, gun ownership, possession, and continued possession should be contingent upon timely filing and payment of Federal, State and Local taxes.

One part of gun ownership should be a demonstrable ability to abide by governmental laws, and clearly, EVERYONE is supposed to file.

So, just require a simple tax clearance from the Fed, State and local governments  before allowing someone to buy a gun.  It'll clear out obvious scofflaws.

Same with continued ownership. Make people re-certify tax payment compliance yearly.