Unless I misunderstand what you mean by absolute, I don't hold "rights" as anything other than a societal convention. The US Constitution isn't holy scripture, it's some ideas some guys had that they wrote down and voted on. The same process can be used to modify it.
I inserted a phrase to correct your logic.
The highlited phrase and the underlined phrase are saying two different things. One doesn't mean the same as the other. For example, we absolutely know that eliminating guns also eliminates gun violence. How? Two ways. The first is as a logical consequence, but we also have an experiment in play. Guns are forbidden in prisons. There is no gun violence in prisons. So, yes, no gun violence follows from no guns. The best you cold probably support is that very weak gun control doesn't work. But then I'd say it wasn't gun control at all, since "control" kinda implies something that actually controls.
But then you switch to "viable solution" instead. This, of course, is a matter of opinion - what would we accept? That's an open question and the answer changes over time. Certainly there are things we accept now (restrictions on our freedoms) that we didn't in the past - for example environmental regulations. There are also areas where we've become more permissible. The landscape here isn't fixed.
I think we part ways here if you imagine the government is somehow a separate entity from "the people." Abraham Lincoln's quote was: "Government of the people, by the people, for the people, shall not perish from the Earth."
Like Soylent Green, it's made of people and isn't a competitor. What it is, and all the restrictions placed on it, is a job description. There's no particular reason you need to do the job yourself. If you want a gun to prevent law breaking, become a policeman. If you want a gun to protect your country, join the army.
This idea of becoming a government of one and sovereign by dint of firearm has a name - it's called anarchy.