Just a thought: If the constitution prevents things that would work to prevent this problem form reoccuring, maybe the constitution needs fixing. After all it is rather old and contains a whole bunch of other bugs as well.
However right now trust in the government is so low that even if the constitution was amended many gun owners would probably be unlikely to accept the result.
2/3rds of each house, 3/4ths of the states
You might get agreement on that point. You won't get agreement on what the bugs are, though, so fixing them by changing the Constitution is rather difficult.