Of course I have a main AD, and we are also very good friends, but I can buy at other ADs if I like a specific piece (e.g., the AD where I recently bought the 5131P was a new one for me). I just think it's good for both parties in this type of relationship if there are more options (for instance, several ADs in Italy now invite me to events, or offer me nice watches, etc.).
I never heard of an AD holding up the documents of a watch, especially on such a good client as you. Quite frankly, I would start looking around for other ADs as well; that might both speed up the release of the 5131R documents from the UK, and also open up new opportunities for your collection...given your high standing with Patek as a company, I'm pretty sure it won't take you long to start getting limited editions elsewhere ;-) Cheers.