From my practice books, I think I'd do decently on the ASTB, but I'm sure I could do better with more study time, which is why I'll probably take it twice.
I called the Officer phone number on navy.com, gave him my info, and then an enlistment recruiter called me back but didn't know I had talked to anyone yet. I think this was because I "requested more info" at the same time I called them, so he was probably replying to the website request, rather than following up my phone call, if that makes sense.
I'll call and set up an ASTB though, hopefully they'll put me in contact with the right people along the way.
Thanks again for all the replies.