......Annual licensing, tied into a criminal/mental health database is the most likely mitigating measure, I would think. The occasional crime of passion would remain a very real threat, as it is now.
How about adding to that making it a criminal offense to allow your weapon to fall into the hands of children, including your own? You could wrap that up in all sorts of caveats (making an exception for kids at licensed shooting ranges, for instance). The designed effect would be to encourage people to store their guns safely at home, in a place where children couldn't get to them. This as an alternative to a registration scheme with safe storage requirements and police checks, which some people would resist.