"I'll ask them about insurance"
See if you can get a copy of their policy. Talk to people that do events in that park. It might be worth purchasing an hour of legal time to make sure you will not be liable for anything. Be careful about assuming liabilities.
2000 Montague CX, I do not recommend it, but still ride it.
Strida 3, I recommend it for rides < 10mi wo steep hills.
2006 Rowbike 720 Sport, I recommend it as an exercise bike.
1996 Birdy, Recommend.
Wieleder CARiBIKE (folding), decent frame.