As the flagship iconic property of the flagship iconic Hilton brand, the W-A doesn't really give a hoot about elite status or how many nights someone stayed in Peoria.
You can book high-end rooms, UG to high-end rooms or deal with standard rooms which are still generally very nice. It's not a trendy hotel and it's not meant to be.
The best way to get great rooms at the W-A is to be really nice and pleasant to the FD and make the ask in a polite and informed manner. Don't ask about UG's, but ask if there's anything nicer available. Don't mention status ! (In NY, status means you're in the Social Register).