While your suggestions may be palatable to the right, they're still a waste of political capital and simply ineffective. Offer something meaningful.
Maybe starting on the civil side is where we need to go. Whenever you hit a business in their wallet they change to make sure their wallet doesn't get hit. So, let's start by making any seller, private or commercial, liable in civil court, to the victims that suffered by the use of what they sold. You want to massively change gun culture in this country, that would do it without changing on a policy level, the perceived constitutional right to own these weapons.If you want to go one step further, make the manufacturer liable too. And I'm not saying possible liability, I'm talking strict liability. If a hand gun or an assault weapon (for example) is used in the commission of a crime then the seller and manufacture are both strictly liable for all civil damages, jointly. You would see manufacture and seller instigated safeguards in these things faster than any other way.
We could also attach criminal and civil penalties to parents whose children take their weapons and use them. Wouldn't have helped in the Connecticut situation as the kid killed him mom, but she was the "gun nut". If you want to be a gun nut (and I mean that with respect) then you bare the responsibility if your child - or even anyone on the planet - uses your weapon in a crime.
Legalize and decriminalize many drugs. Yes, that one hits this topic too whether people want to admit it or not.
Mental illness does need to be addressed. I'm all for it for a myriad of reasons. I have no idea how to begin, but I'm willing to listen to anything.