I agree with you, that the American attitude towards guns is the main problem, but there is no short way to fix that.

The only ways to change the attitude of an entire country, would be to either hold awareness (read propaganda) campaigns like they did with cannabis or to educate the next generations on the dangers of guns and wait for the older generations to die out.

If you want to diminish the shooting counts, restricted gun owner ship US wide with background checks would be one step in the right direction, I think.
But there is also the problem of all the people, that own guns today. Just enacting gun control would make a lot of those guns illgeal possessions and could therefore potentially create a giant blackmarket. You would have to thin out those guns somehow. I could imagine a campaign in which the state offers gun owners compensation for their guns, just to throw in an idea of my own.