We had the same complications with booking three rooms. My in-laws tried to put the charges for their room on their card, which the concierge at the Poly said had been done. In the end, it was all charged to my card and they ended up writing us a check as well. It took us about an hour to check in all three rooms, due to the payment issue and wrong room assignments (two garden view and one lagoon view), but I honestly don't think this is typical. It's well worth it for everyone to get the AP rate.
If you get a CM who tells you that you can only book one room (I did the first time I called) just say thank you and call back until you get one who knows that you can book three rooms.