Ok. This is where my memory of Constitutional Law breaks down a little...
Even after you establish the "strict scrutiny" standard for a right, there are different standards that the State must prove if they wish to infringe on that right. If you're a "protected class" of people, i.e. a minority, then the burden of proof is extremely high, something like "absolutely necessary to accomplish a compelling governmental interest," and the law must "only infringe the right so far as is necessary to further the compelling governmental interest." (This is all REALLY fuzzy...) If the law is not targeting a "protected class," then the burden of proof for the State becomes lighter...
More questions:
1.) Are "gun owners" in a protected class, since anyone in the country can own a gun? In other words, are we a "minority"?
2.) Does the government have an "interest" in restricting use or ownership of firearms? (The answer to this is most assuredly, yes. The interest is the reduction of crime and the prevention of unnecessary death and destruction... blah, blah, blah...)
3.) How "compelling" or "important" or "strong" is the government's interest in preventing violence?
4.) Is there a clear relationship between restricting use/ownership of firearms and a reduction or prevention of violence? Will the restriction proposed actually serve to further the government's interest?
5.) Does the law do more than it says it does? Does enforcement of the law result in people being excluded from gun use/ownership who are not the kind of people the law was designed to exclude from gun use/ownership? Does the law go too far?
The analysis for the "strict scrutiny" test will require answers to all of these questions...