The basin and range distribution is particular to firearm suicides.
Those are rural places, with limited access to healthcare, cultures of shame around mental health, limited economic opportunities, and high rates of gun ownership.
I have no way to know causality, but my guess is that the social factors are far more important than the barometric pressure.
Most of those social factors you've listed are things that are influenced by base transportation costs, so I wonder if there are similar patterns in other places with gun ownership and varying topography: Australia, Canada, Russia, Southeastern Europe...
Those are rural places, with limited access to healthcare, cultures of shame around mental health, limited economic opportunities, and high rates of gun ownership.
I have no way to know causality, but my guess is that the social factors are far more important than the barometric pressure.