Also, fix the criminal justice system to encourage criminals to be unarmed.
This is an excellent idea that other countries already use. Making punishment for crimes with firearms far more severe than the same crimes without firearms. So that it discourages criminal gun use.
It would need police to be better than they seem to be right now to make more efforts to de-escalate rather than push an emotional or disturbed to violence that could have been avoided. This is key - if criminals think that will get shot anyway, they will feel the need to be armed.
Yes, this is a problem. It seems that police academies currently teach officers to "take control" immediately and totally in all interactions with civilians, but as we have seen in recent years, this strategy is unnecessarily aggressive, and turns out very badly when they are confronted with an angry or irrational citizen. The police really do need to learn when to 'back off' and let non-compliant citizens have their way when they are not otherwise presenting any danger.
Increase the differential in sentencing for those heavily armed/lightly armed/unarmed, so that carrying a gun might seem more risky for those habitually getting arrested.
Crimes involving violence, or a serious potential for potential should be treated more severely, I agree. While non-violent crimes should be less so.
Limit access to assault weapons, concealable weapons and those that are more lethal, such as high velocity ammunition. Householders would be better off with shotguns, for example.
There simply is no logical reason for the average citizen to need these. They should be allowable only to those who have the purpose and training applicable.
Destroy all confiscated firearms, instead of selling them on, to reduce the black market of untraceable weapons. Register all firearms and require licenses, testing and reasons.
Yup, we are swimming in these guns, now. We need to destroy millions of them. But not those that are properly licensed and registered.