There is estimated to be about 400-600 million guns in the U.S. The majority of them are probably semi-automatic weapons at this point. That is a gun to person ratio of between 1.2 and 1.8.
Controlling the supply of guns is just not logistically possible at this point.
It would be easier to:
Introducing every point on this list would be easier (and likely have a greater effect on shootings) than reducing the supply of guns in the U.S. Solving these problems would also solve many other social problems in the U.S as well.
What you have listed is so naive... Seriously, have a school psychiatrist evaluate every student? Then what? The ones with potential problems gets sent somewhere or keep on receiving therapy? That will somehow prevent people from snapping and go on a rampage? People snap all over the world. The USA problem is guns are readily available for the snappers to do mass damage. They like to broadcast it too and brag about the mass damage they are able to cause.
In denial, putting bandages on instead of curing the problem. 600million guns, so what? If you start now and have some sort of normalcy with guns ownership, that number can be 300million in 10 years. In 20-30 years, may be USA can become a normal country where people aren't getting shot daily. Once you have guns under control, may be then police aren't scared the shit out of every time they inspect someone and police violence will be solved as well.