You buy insurance for this kind of trip, part of that insurance goes to paying rescue costs. Generally $100-200k is enough for private rescue. Otherwise, yes, the Navy and Coast Guard have units solely dedicated to at-sea rescue.
Yes, I don't know if they transmit any kind of individualized information though, like a serial number. But as it stands, what sort of incentive do rescue workers have to actually find you? I'm willing to bet they get paid either way. The trick would be to place some money into escrow as a bounty to the one who finds you.
What's the point of being wealthy if you're treated like just anyone else?
I don't have the confidence that they will.