Weapons regulation is certainly a charged and polarizing topic in the US. It's difficult to discuss without people having extreme emotional responses. So let's jump in... :-)
The 2nd Amendment text is:
A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed.
It's obviously not too clear, or we wouldn't still argue about it. What's the whole militia part? And even if it was clear in saying people have the right to keep and bear arms, what are arms? Are arms just the musket loaders, bows, and blades that were available at the time that this sentence was written? Or does arms now include the hydrogen bomb?
How about this approach. Change the 2nd Amendment to be clear (i.e. "People have a right to keep and bear arms"*), then define arms. And make sure that arms is not a static definition, because weapons technology changes all of the times. It's hard to imagine that the founding fathers could have envisioned biological warfare, missile wielding drones, or even a taser.
How to define arms? What restrictions on arms should there be? Certainly not the goofy restrictions we have now - like whether or not a gun has a bayonet attachment or pistol-grip - that's irrelevant. How about basing the restrictions on things that matter for the practical use of them, which for the populace would be defending your home and hunting. I posit these criteria for arms restrictions:
1) Lethality per activation.
In other words, how many people would activating this weapon likely kill per activation. (I'm using the word activation instead of trigger pull, because I'm not talking about guns specifically, just arms.)
Most guns/rifles, bows, blades would have a lethality of "1". A grenade would have the lethality of ">1". A nuclear device would have a lethality "> 100,000". Pepper spray, slingshots, tasers, etc. "<1".
I'd argue that "1" is the appropriate value.
2) The rate of weapon activation.
This is how quickly the bow can shoot the next arrow, how quickly the bullets can exit the gun, etc.
I'd argue ~10/minute is sufficient. It's certainly overkill for hunting. But for home defense, let's say a gang of 4 enter, you're @ 50% hit rate, etc.
Greater than 10/min would be things like semi-auto weapons with large clips (because reloading would be taken into account for the rate), fully automatic weapons would be out, etc.
3) The distance of lethality.
This would be defined as the distance from where the device is activated to the location of the lethal event. So, for a rifle, it'd be the bullets effective range. For a bow, it's the effective range of the arrow. For a missile wielding drone, it's the distance from the remote control to the target. For a nuclear device it's the blast range.
I'd argue that ~hundred yards is sufficient. Clearly that's sufficient for home defense, but not enough for longer range hunting. But there could be a trade between #2 & #3. Longer range? Then lower rate.
Lastly, self-inflicted deaths (whether accidental or suicide) prevention is a worthwhile goal too. Hence protective caps on medicines, safety measures on power tools, etc. For firearms, where most gun deaths are suicide with hand guns, having a minimum trigger-to-barrel length that is greater than the distance of the average arm would go a long way to preventing suicide. (And of course keep a safety on the weapon.)
Okay, the "unsolvable problem" is what to do with the hundreds of millions of guns currently in the US? How about this:
Now that arms is somewhat defined, also define new firearms to fire a caliber(s) that is not currently on the market. (Or maybe it's an old caliber,(s) but have a casing that is shaped incompatibly with current offerings.) Then sell this new caliber, but bar selling any of the old calibers. A trade offer for "old fire arm" to "new fire arm" could take place too. But, allow people to keep their current firearms, knowing that once the ammo is gone, it's just a collectors piece.
*People would need to be defined too, excluding felons, toddlers, crazy people, etc.