If the condition of the boat and sea state does not put the coast guard vessel in harms way, get all non necessary people off of your boat and look the coast guard skipper right in the eye and tell him with authority in your voice:
"I am the skipper of this vessel. If you want to save me you have to save the vessel."
Right. Maybe it'll work with a 60 footer, and I have doubts, but with a beach cat? The coast guard skipper is more likely to "inadvertently" drive over one of your hull before plucking you out of the water. Apologizing for the damage of course. Not to mention that you are assuming that a boat came out for them, from what I heard an helicopter was involved, it's hard to tow a boat from an heli (Alinghi did it, I know).
Depending where you are, if what's left of the boat could be a danger to navigation the coast guard also have the authority to sink the rescued vessel. And they'll do it.
