In the true spirit of compromise, where both sides give up what they really want in exchange for something closer to what the other side wants, I would propose a bill that...
existing federal level firearms laws.
2)Specifies that the 2A is incorporated against the states so the states have 2 options: 1)Shall Issue Permits based solely on reinstituted NICS check. 2) No permits at all, i.e. Constitutional Carry.
3)NICS check for all firearms transfers between "unknown" persons. Unknown persons defined in a manner similar to the current "prohibited persons" standard, such as seller and buyer have "reasonable history of having known one another, such as but not limited to co-workers, neighbors, relationships between children, etc." All family members out to 3rd cousins, through genetics and marriage, are "known" persons.
4)Prohibited persons are those who have been convicted of a violent crime of some "X" minimum standard and within "X" time period for minor violent crimes, like "mutual combat", i.e. a couple guys got in a fist fight. "Coming to blows" when you're 21 and drunk should not be a life-time prohibition. No other person can be prohibited for any non-violent crime.
I might have more, or modify that list, but it's a start.
Still happily answering to the call-sign Peetza.
You do not HAVE a soul. You ARE a soul. You HAVE a body.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.