Their constitutional rights trump any government interference - that is why it's in the constitution.
Another great example of how a law can sometimes be an ***.
Just because it is constitution doesn't make it correct, but what is the solution?
To me; the problem is the bullets.
Anyone can own a gun, but without the bullets to fire, they are useless. We can make it very hard to acquire and own a gun...make it just as hard - or harder - to buy the bullets without good reason.
I think on thing which may help is to make every bullet purchase needing a registration like the guns need to be.
And. with a limit of say; 6 only at any one time - no matter what the weapon, and all records of purchases sent to the respective law enforcement agency to monitor. All bullets to have a matching batch registration number.
No further purchases allowed to be made until those 6 are used (so; potentially a froot-loop could take out 6 people with their ration, but highly unlikely).
All bullets fired by that weapon, or used by others or in another gun, would need to be declared to the respective authority by the registered owner of those bullets, so they can monitor the amount of bullets you have left to fire...
Random audits are then conducted without warning to inspect the registered guns and bullets - If an audit finds bullets missing, the registered owner receives a corresponding penalty. I think immediate confiscation of the gun and bullets, and a hefty fine - for the first offense.
Anyone wanting to buy more than 6 bullets at any one time, or before their current ration has been used, would immediately raise a red flag at that respective agency and then investigated.
Of course; the dangerous folk would look at finding ways to get around this, as they always will, but the process for most ordinary folk who just want to own a gun for protection - or young guys with a gripe who would potentially be a candidate for a spree shoot - it would be a "too hard" thing and hopefully stop them before it's too late.
edit: this would also apply to the components and/or ingredients with which to make bullets....volumes of ingredients purchased only enough to make 6 at any one time, all recorded and registered with the authority, as per the above guidelines..
There ya go; a whole new arm of employment created for the Government - folk to administer and manage the new registration system.