The only AA flight numbers to GOT is a Brussels Airlines flights from Brussels (which I'm guessing you've already figured out
) It looks like this causes you two problems, one you already know about and one you may not:
1. AA only flies non-stop from ORD and JFK in the US to BRU. Unfortunately, it appears the ORD-BRU flight arrives in BRU too late to be a legal connection to GOT. So you would have to connect through JFK which, as you discovered, has no non-stop AA service from CLT.
2. If you are coming back after March 28, 2010, this flight routing will not be available to you on AA flight numbers, since AA's codeshare agreement with Brussels Airlines ends on March 28, 2010
There are other types of awards available such as 'all-partner' awards and OneWorld awards, which would allow you to use award mileage on AA and its partners, and do not require you to stick solely to AA flight numbers. AA's European OneWorld partners are British Airways (no service to GOT), Iberia (no service to GOT) and Finnair (service from Helsinki-GOT). Finnair flies from a couple of US cities (JFK, Boston seasonally, MIA seasonally, according to wikipedia) to Helsinki. So, you could try to route CLT-MIA-HEL-GOT where CLT-MIA is AA (American Eagle) and MIA-HEL-GOT is Finnair. This would only work when the MIA-HEL service is running, of course. Otherwise, you'd have to route through JFK.
I am not an expert on these partner/oneworld awards and will defer to the FAQ and wiki for you to find more information (full disclosure: I've never personally booked one of these types of awards). You will have to call AA to book an award of this type, they can not be booked on-line.