I am personally a fan of another a solution along another axis entirely: a complete overhaul of our medical system, notably in this case the way we detect and handle the mentally ill. (A part of that could be mental evaluations for those who want to buy guns.)
>>jlgrec+(OP)
This seems like the right approach, but part of the overhaul needs to be a massive increase in research. We don't have a good way to treat the mentally ill, in most cases.