I believe that it will take a bunch of different cultural changes to mitigate mass shootings. Its a very tough issue because the root cause is the mental state of the would-be shooter. Here are a few of my thoughts on the matter. Fair warning, many of my views are very, very conservative.

• I think that peaceful and engaged parenting should be much more widely encouraged.
• Two-parent households need to be held up in our culture again. IIRC many of these shooters are male and are from single-parent households.
• The incentives for having a single parent household needs to be reduced.
• Public schools should be avoided if at all possible. Homeschooling, cooperative schooling with other parents, and small private neighborhood schools can reduce the incidences of bullying and decentralize would be victims.
• Gun stores and mental health professionals should work together. Maybe it should be an industry standard (NOT GOVERNMENT MANDATE) that gun stores do a mental checkup on new gun owners before selling the guns.
• Gun stores should also have pamphlets and references to mental health professionals on hand. (AGAIN NOT GOVERNMENT MANDATE)
• Mental health and counseling should be more widely encouraged. To the point that its as normal as a routine physical checkup.
• Hookup culture needs to be demonized and discouraged. Sex needs to stop being seen as a mere recreational activity. This will reduce single parent households and choke the fuel for incels.
• News agencies need to stop putting the names and faces of these shooters in their reports. They ought to be shamed into this. It makes the shooters infamous and gives more morbid motivation to other shooters.
• Digital minimalism should be widely encouraged. Addiction to social media can exacerbate mental issues and worsen political extremism. Technology is a tool, not a way of life.
• Political power should be decentralized, not centralized in one entity. The centralization of political power is what causes political extremism to rise. This will reduce political terrorism.
• Prohibitive gun laws need to be struck from the books. Mass shooters will get their weapons one way or another and the populace will be left defenseless.
• Place where potential mass shootings can occur need to either have well trained guards, police, or have an open carry policy. Yes this even includes schools.
• End the war on drugs. Legalize it and culturally discourage drug use. Mass shootings due to gang violence is often ignored. Many of the things I mentioned above will also help gang-ridden communities.

This is getting long so I'll end here. OP is right that this is a complicated issue. However we do need to recognize that we need to tackle its root causes, not the symptoms.