Lee,
If all ORA's are gated and guarded it kinda smells like an inside job to me. If you are staying for a while you might put out the word you are interested in buying a golf cart. Also check on any local golf cart outlets to see if someone is using one of them to fence the stolen goods. You might also check in with local golf courses to see if anyone has approached them about this great deal on a golf cart that thye could pick up.
Sorry to hear of your misfortune. As for the dogs daily ride in the golf cart you may have to rent one temporarily.