Freedom of speech does include slander; slander (and all other defamation) is not a criminal matter, it's purely tort.

Freedom of religion does not protect abuse

Oh buddy... Have I got some really, really bad news for you. SCOTUS has been continually carving out exceptions for both criminal and civil law for religions for decades.

Should addicts be permitted to carry firearms?

I think that it's a very, very slippery slope to try and traverse. I've known people that were entirely functional alcoholics; they were entirely sober all day, but started drinking the second they got home, and all weekend. I know a guy that holds a solid six figure job at a major US company that has spent literally hundreds of thousands of dollars on drugs, and tanked multiple marriages because he couldn't straighten his shit out in his personal life, but he is solid for his rationality as long as he's sober. Which is pretty much only when he's on the clock. I know people that are straightedge that are less able to think rationally than either of those people. So, should we have a rationality survey prior to someone purchasing a firearm, voting, getting legal representation, refusing to talk to cops, and so on?

But here's an even bigger problem for you: barring addicts from owning firearms--or people that have been committed to a mental institution for any reason--is actively dissuading people from getting help. If you are, for instance, a cop, you will lose your job if you can't own a firearm. The result is that cops don't get help when they need it. Many gun owners feel the same way, and there are grass-roots organization that will hold parts of guns for you (non-serialized but essential parts) for people that are having a hard time but can't seek help without losing their rights.

The problem with my argument is that I don’t think our restrictions on gun ownership go nearly far enough.

No, the problem is that you're treating a symptom--violence--as though it was caused by the tool used to commit it. The problems are things like systemic racism, chronic underfunding of essential services, shitty public education (that's been made intentionally shitty to try and steer the "right" people into charter and private schools), lack of economic empowerment, wealth inequality, lack of reasonable access to healthcare, and so on. It's treating pneumonia with cough syrup, and then wondering why shit doesn't get better. (And, BTW, despite the massive uptick in firearm ownership that happened in 2020/2021, violent crime, including gun crime, continues to decline.)