Well this seems a bit contradictory.
*or* accept that prevention is nearly impossible and instead focus on reducing the likely body count when such a shooting occurs, which may by itself deter some shooters from bothering in the first place.
You're failing to understand that there's no way to prevent someone who wants to kill a bunch of random people in a public space, unless you can put that level of security in *every* public space.
Well that is simply not true. I mean, sure, there's not a whole lot you can do to find them once they set out to to kill people, but that doesn't mean they can't be stopped from ever going out for a killing spree in the first place. There's a few effective ways to do this, but i guess you probably won't like any of them: Better education, better support for the mentally ill, more help for the poor, and of course restricted gun access.
Restricting gun access makes it more difficult for people who want to go out and kill a bunch of people to do so. Unfortunately, you're right, this isn't such an effective method. It would certainly help, but not all that much, unless done to such an extreme that it's a waste of time to even discuss, because as you said, it will never happen. Of course this doesn't really get to the root of the problem. Even without guns, people can still do a lot of damage with a knife, or bombs which can be made out of common houseful supplies. The solution isn't to physically stop people from killing each other, it's to make them not want to do so in the first place.
That brings us to the mentally ill. Sane, well-adjusted people do not just go out and shoot up a mall for no reason. It just doesn't happen. We need to stop treating the mentally ill like garbage, and start getting them help. And that doesn't just mean finding them and stuffing some pills down their throats. They need real support, and right now we do almost everything we can to ensure they cannot get it.
Improving education and help for the poor is just a no-brainer. The uneducated and poor are both much more likely to commit crimes than the rich and well educated. There are many reasons for this, but the solution is simple. We need to provide much better education, including (especially!) for the poor. Educated people are better people, in pretty much every way so this is really very important, and will improve society as whole in many different ways. The poor have more to gain, and less to lose from committing crime, get worse education, and often have no real access to mental health services, so it's no surprise they tend to commit more crime. I'm sure we already know how to improve that situation, so i won't bother covering it.
These are the things that matter. Improve these things, and crime will drop across the the board. Not because people are unable to commit the crimes, but because they no longer want to. And that is how to stop shootings. Not with metal detectors and strip searches to get into a McDonalds. Not by repealing the second amendment. And not by giving everyone guns so they can kill a shooter before they kill too many people. You do it by making sure all of society is healthy and happy.