On Sept 9 and September 15, both American and US Airways took jumpseaters between the US and Grand Cayman. I was down there with another pilot and we both jumpseated both ways. Can't help you with the current policy, though, I'm no longer working for a 121 carrier.
Try the Hyatt Regency on Seven Mile Beach...airline rate of $99 per night.
If you want to go to Cayman Brac for a day trip, go to the Cayman Airways office on Grand Cayman and buy an ID 90 for $10 roundtrip! You can't get this deal from your own airline, like other ID 90s. You have to buy it directly from Cayman Airways.
Cayman Airways won't take jumpseaters from the US unless you talk to the captain directly. Gate agents and ops personnel automatically say no, but the captain has the authority to override this.