You can't fully stop them but if you did the following three things you are likely to see marked improvement.
Do away with gun free zones. Near-suicidal maniacal types will no longer believe they can go to certain places and find themselves a bunch of defenseless victims. This bloody lottery they will find themselves playing anyhere they go may deter some. And if one goes off, hopefully he will encounter a proverbial "good guy with a gun".
Address the issue of excessive SSRI use.
Work on addressing the lack of male roles models in the lives on many boys.
I personaly think you should get a license to be able to buy a gun. Same as driving license.
I do agree though with all your 3 points.
In Massachusetts you absolutely need a license to legally carry a gun. But even with a license you are breaking the law if you come on school grounds with your gun (if, say, you need to go there to pick up your kid from school).