Trey, you are a lucky man! You stay at one of, if not the, best resort on Phuket. I love the place!!! I do not have the money to spend to stay there but have been lucky enough to enjoy the company of people who can. Only the best here, great place. Laze by the pitch black pool in daytime, have great cocktails at the bar overlooking the private beach, dinner at the Italian or Thai restaurant with appropriate music, it is all good. Not coming cheap, but if business my best guess is that you would not care to charge to your room....
As for moving around. Use one of their limousines and have you dropped off at a reasonable hotel for an 'appointment'. This way you might avoid any talking from staff if you want and can move easily to one of the massage joints described in other treats, or go to Christins for a soapy.
I am for 99.9% sure that Amanpuri is guestfriendly. In the good and real good places you 'rent' a room, not just a part of the king size bed in that room!
Just relax, enjoy the hotel, and enjoy any good (!) massages. I wish I was in your shoes!