Hate to break it to you, but most women aren't going to be interested in spending a week sharing a cabin with a man they don't know... especially one with little or no track record or reputation to base any opinions on. This is your first post in an long-standing on-line sailing forum, and my response is very likely to be one of the milder ones.
$2000 for a week is pretty expensive as well... I see very little upside for any woman considering spending a week in the Caribbean, compared to say going via a cruise ship.
Also, saying that you're looking for a fling, and then saying it could be platonic a sentence later... really makes your post questionable IMHO.
Personally, I think it'd be far easier to respect your position if this wasn't your first and only post on the forum to date—and you didn't come across like the typical "looking for hot female crew" poster on this forum, but it is your first post, and you do come across that way...
That'd be far more reasonable than what he is asking... I don't know about you, but I'd be a bit wary of sharing a cabin with anyone I just met... there ain't enough privacy on a small sailboat to begin with, much less when you have to share a cabin with a total stranger. The fact that none of the people he knows are willing to go with him says a lot IMHO, and not in a good way.