I believe that stricter gun laws won't change anything. Criminals are criminals and they'll find their way no matter how strict our gun laws are. What I think we need to focus on is the process in which the mental state of each person is monitored. The best thing anyone can do is to have a family member have a way to report discretely about their child or relative who's not "happy" and is purchasing guns.
I don't believe that gun control and respect for the second amendment are mutually exclusive. Criminals are going to get guns, sure, but laws that say you don't have to do any kind of background checks for private gun sales means those criminals are buying their guns legally. Straw purchases are illegal, but our ability to pursue people engaged in the practice is limited. And that does not address the problem of loaded guns being left around where anybody can get at them, and children shooting each other. These incidents are always mourned as tragic accidents, but they are treated as accidents rather than criminal acts of negligence.
The goal is not perfection, because we're never going to get there. The goal is reducing the amount of gun violence we see on a daily basis. Your point about mental health is a valid one, considering that the majority (2/3) of gun deaths every year are suicides. It is both easier and cheaper for someone who is depressed to buy a gun than it is for them to seek help, and that has got to change. Moving to a single payer health care system that includes mental health care would be a huge step in addressing that problem.
We have to address both problems. Suicides and homicides, while both frequently use guns, have different root issues that we need to deal with. That means research, which means we need to end the ban on CDC researching gun violence. We should not simply accept this tragic situation as the "cost of living in a free country" because it *isn't*.