RE: State Parks
Tim, you're covered anywhere you have the land owner (or regulating agency in this case) permission to fly and you fly in accordance with the AMA safety code. The AMA insurance is supplemental to any type of home owners insurance you have as well.
Suitable home owners insurance would probably suffice but that opens up a mess for whomever is running a site. Verifying coverage with AMA is easy. If you have the right colored card, you paid for the year. There's lots of cases in auto insurance where people start a policy, get registrations and drop the policy so they have the card, thats not possible in our case since you pay the full amount up front every year.
The key to happy relations with site owners (unless they themselves are modelers and understand) is to show them they are covered for liability, keep their administrative over head to an absolute minimum, and not put them in a position that people are griping about noise or fly over issues. To most people, complaints about noise, percieved unsafe operations etc just aren't worth the hassle and they would rather close a field to flying than deal with it.
Put a parks department in the position to be mediators or checking insurance cards etc and the only thing flying there will be the birds and the occasional kite.