An AMA alternative ?
An insurance company already exists that offers individual, field, and event coverage (UMA). They have operating for a year or more, so we know it has a chance at being viable. However, I'm not aware of a huge number of clubs signing up with them.
On the event entry issue: There is more to sanctioning an event than insurance, particularly if it's a competitive event running to nationally recognised rules. It's not unreasonable that a sanctioning body require you to be a member of that body.