Honestly, what I would recommend is focusing elsewhere for now, as Spider says (and I shudder at agreeing with anything he suggests).
Ending the War on Drugs would cut mass shootings in half. Redistributing wealth in a meaningful and sustainable way would decrease it further. In the meantime, put together a coalition of 'Repeal the Second' advocates, who have the guts to pursue that measure (and it would be very unpopular for a time). This will be more effective and more doable than pursuing more regulations on guns, which if even passed, will have a minimal impact on the murder rate.