Have the EPs make the backstage area more restrictive when possible (ain't that bad an idea for a NUMBER of reasons, this being one). Athletes/Coaches/Gym Owners ONLY, may ONLY go back if checking in with a team that needs to be there. Maybe 1 to 2 passes per gym TOTAL may be given to additional people (if Team Moms need to go with them), and can only be given to adults registered with the gym, proof of ID required if attempting to go into the area. Teams are funneled from the mat to a designated area before moving back to the arena. That's at least a few set areas where you can keep things down a bit.
You don't want to completely cut kids off from interacting, as that's a social function and it'd be a shame to lose that connection (I just think of that photo with the F5, WC and SE girls at college)..but at least make it less open to chaos.