There's no way around it, if you want to change the constitution regarding such an important aspect that deals with states' citizens having the arms to organize an armed resistance against the federal government's standing army should the need arise, then only a broad and honest discussion within the US-society followed by a general referendum can do the trick.
If the US-society decides in the referendum that the right to have arms in citizen's hands is too important to give up, then that means it accepts the price of crazy people using these arms to cause havock every once in a while.
The reason why imho a referendum is necessary is because getting rid of that right to arms means to forcibly disarm the population. Such a drastic move needs considerable legitimation that only a referendum can give.
That would seem to be a convincing interpretation if the proposal were to disarm the population, but what about the grey area in between? The right to bear arms is already not unlimited. If the proposal were just to tighten the requirements for background checks, registration and storage, rather than disarm, would that still apply? Presumably not, since the constitution does not address such details.