How many times are we going to find out someone had a history of mental issues and nothing was done? How many people are reluctant to take proper medication because they view the effects of the medication worse than what it trying to treat. We have a lot of people coming back with PTSD, we need to get better at this.
I remember OK and that was farm products (which some companies still sell at automated machines). IEDs, pipe bombs, propane canisters, Molotov cocktails are all capable of killing a lot people and are easier to build or acquire than guns.
But mental illness itself has no check point. How can we ensure that people do not have untreated Schizophrenia? Mandatory checks for everyone once a year? I'm really not sure how it could be done.
We haven't put the money into brain research to figure out if there is a test we could do. Checkpoints are the easy part. Look at all the places we test for drugs (employment, school sports). If we figured out the mythical dipstick that tells if your brain chemistry is broken, I would imagine it would come up in a lot places that drug testing does now and probably be part of peoples regular checkups. We just don't have a clue and no amount of dealing with the how will fix the problem, we need to get the courage to look at the why.
Regardless of ones position on guns, it's almost universal that not nearly enough who need mental health care get it. And, our national attitude is still one of "Therapy is for crazy people!" - yeah, just like "the ER is a viable form of preventative healthcare" and "you only go to the mechanic when your car is on fire".
I'm a libertarian but in practice I'm not sure of a solution that isn't more government involvement.
EDIT: That article you linked to discusses a 3d printed lower receiver. That part of the rifle does not have the barrel and chamber. The part of the ar with the barrel and chamber is called the upper.
You can't ensure that every single person that has a mental disability gets treatment, but as a society we do not support easy access to mental health treatment. Mental health services, like physical health services, are pay to play and that provides a huge barrier for people with mental disability, esp. since some amount of those people will have a very hard time affording such treatment and/or medication. Consider also that folks with mental disability tend to have less robust support networks of family of friends and that mental health care has stigma attached to it for most of the US population.
The best option is to reduce the difficult of getting mental health care treatment as much as possible: universal health care, public awareness campaigns to fight against social stigma, and more robust social services.
Do all of that, and anyone who tries to buy a gun without a license can safely be assumed to be up to no good. You don't even need to license firearms themselves, which is unpopular.. just the owner themselves.
Most of these nutters are buying their guns legally. Hell, I bet a lot of them buy their guns not even fully realizing what they will eventually do with them.
Illegal sale/ownership of guns is just an issue for the police to handle. I don't think there is much progress to be made on that front.