How about this since the left loves diversity politics we do this:

Set a # of shooting per 100,000 people limit and we divide people out in the following way: (Any group above that limit has to go through an FFL dealer)
1) Race
2) Sex
3) Sexual Orientation
4) Age

For instance:
A 0-100yr old Straight Black Woman = can buy a firearm because her score is < the limit
A ________ ________ ________ _______ = can NOT buy a firearm except through a background check because their score is > the limit

A CCW overrides all of these limitation.

Use the "we can't discriminate against women since men do most of the shooting" argument to make the left twist themselves into a knot.