I think that Charmion's idea (6:49 AM)of requiring all gun owners to be members of the National Guard is a good one. That would ensure that anyone 'packing' has had training in the use of weaponry and counseling in the utilities and ethics thereof and that could only be a good thing.
Further, some people might well decide that the requirement is too onerous or restricting and give up their weapons.

Most importantly, it would be a start. A start in meaningful dialogue. And just maybe it would be acceptable to the NRA/gun lobby.

(Far off topic: I wish people would be more aware of the difference between 'discreet' and 'discrete'. The misuse always sounds dumb.)