Honestly, if schools want court storming to stop, it's very simple...any fan would be warned that field/court storming is not allowed while teams are still on the court/field.
The schools have security detain anyone on the court too early. They will be identified, and i it is their first offense, they will be fined heavily and banned from sporting events for 1 semester. Second offense, you are banned permanently from the school's sporting events or even kicked out of the school.
That may sound extreme... but the second offense is only extreme IF YOU CANNOT CONTROL YOURSELF. In which case, extreme measures are probably needed anyway b/c anyone who cannot control oneself is more likely to be the violent offenders due to lack of self-control.
Truthfully, if those in leadership really wanted it to stop, the conferences could even require it of their member schools.