” the large majority of gun deaths here are a result of suicides”
This is correct, and across the US the availability of guns is much more related to the rate so suicides than homicides. The 2012 state-specific suicide rates (I couldn’t find more recent data) show that the lowest suicide rates are, in order of decreasing rate, in California, Connecticut, Illinois, Maryland, Rhode Island, Massachusetts, New York, and New Jersey, with the District of Columbia lower than any state. Those are probably the places with the strictest gun laws in America.