Very logical sounding, BK; but still lacking.
If you make mental health care greatly improved, will you take gun rights away from people found to be really dangerous? I haven't heard you agree to that. You talk frequently about FINDING the crazies prior to their committing crimes; but I haven't read you as being willing to disarm them. Needs clarification
Second, you talk about gun training. Is it to be mandatory? You've suggested this. But if gun training is mandatory, then a person needs proof of having had the training. That requires an agency- i.e. gov't- to verify. PRESTO; you've just advocated for gun control. No proof, no gun. Sort of like a driver's license.
"Badges? I don't gotta show you no stinkin' badges".
So your notions still lack something