JollyRoger- Two points here, its simply insane to allow people who could potentially have severe mental illness carry a weapon or someone who couldn't hit the broad side of a barn at 10ft. Thus the only way to negate that possibility is to issue out CCWs with strict weapons qualifications, backround checks, and psych evals.
Then amend the Constitution. Currently it is a right that shall not be infringed. You are asking for infringements.