Just wondering, but why didn't you consider this before you applied? And, aren't you already receiving money from the government b/c of the BDCP program?
I'm guessing there have been other people with the same question as yours, and the answer they found is probably "no."
edit: The reason I don't think you have a chance changing your designator is that you're at the very beginning of the pipeline. You've signed the paperwork, but you haven't actually done anything. Moving you might have been easier in a better economy when the military didn't have quite as many applicants, however, these days the number of incoming candidates is closely watched.
This is about two words away from a total buddy fuck. The fact is that only a recruiter is qualified to help this guy out.
It would be one thing if you were pointing him to some sort of instruction, or could speak from personal experience, or even knew a guy who knew a guy who's sister's brother tried this and failed. But you don't... you just have a bunch of guesses, probablies, and I don't thinks.
Interesting response from the same guy who posted:
"To any and all applicants like I once was, the single most important thing I can name that got me here is persistence."
... in his profile.
For the OP take HALs advice, ask the recruiter. If you really want to be a pilot don't stop looking for a way. It may take you until after your a qualified NFO and a sea tour but there are ways to transition all the way from before you start API until after you get your wings. You're on the right path by starting here... Good luck.