When BAT and BAS rates came out, I could not get a discounted rate at the GF for the weekend just past -- the columbus day weekend. I checked early and frequently. It was, however, available as a "fall promo" rate -- for precisely the BAT rate -- on expedia. So I booked it that way.
The downside of expedia is that you have to pay the entire amount in advance, and you get charged $25 even if you cancel outside the 6 day window. There's also no feasible way to make room preference requests, since WDW reservations cannot (or says they cannot) pull up your reservations to add the requests.
For what it's worth, though, we just got back and were treated exactly the same as if we'd booked through WDW. In fact, we paid for a garden view, and we were upgraded to a great lagoon view with a panoramic view from the MK to the Poly from out balcony. I know there was some suggestion here when BAT rates first came out and people were discussing expedia reservations that they were not treated the same by disney, which wasn't our experience at all. (Your mileage, of course, may vary.)