Disney does sometimes overbook - especially if they end up scheduling a conference and get more registrants than they expected and blocked out for. At this point - they will contact other vacationers to offer a change or an upgrade - after all - would you want to stay with all those conventioneers anyway?
I would definitely check to see if they will upgrade you from deluxe savannah to concierge level at the AKL - they are the same rooms! I've stayed at the Poly, the CR and the deluxe AKL rooms - the deluxe rooms are at least as big as the rooms at the beach club - we had plenty of room for our family of five there - and the fact that we had bunkbeds, with the daybed each of the girls had their own bed, gives the room even more floor space!
The concierge service at AKL is wonderful, and when we stayed there on AP rates - it was only about $35 more/night than the deluxe savannah rates. If you get in - definitely see about signing up for the special Safaris - either Sunrise (done twice - and LOVE it) or Sunset (would love to try someday!).
A concierge room at the AKL is on a par pricewise with the lagoon view rooms at the Poly.
While you don't have the easy access to Epcot & MGM that you would have at the Beach Club - access to MK, AK and Downtown Disney is much better, IMHO. I have had excellent luck with the AKL busses - they don't share with anyone, and they run every 10-15 minutes. I tend to drive to Epcot & MGM anyway - since I have a
AAA Diamond Pass - it beats waiting for a bus with the crowds after Illuminations or Fantasmic!
Good Luck with your choice - and let us know what happens!