Thanks all for the continued helpful dialogue. If reading about this situation helps someone else avoid this mess, that would be great! A few follow-up comments:
-- I have done a lot of buying and selling on forums over the years across many hobbies (fountain pens, golf clubs, guitars, etc.). Through those experiences I felt like I was equipped to deal with fakes/scammers etc. I absolutely was not prepared for the high quality of fakery in the watch world, as this was a minor interest that I was just getting into at the time. I honestly felt that by buying from someone posting the watch openly on this forum, someone with a normal FB account, whose info/profession/etc. was easily obtained via Google, etc. that I would be safe (and in the event that there was a problem, it would be easy to resolve). Lesson learned!
-- I admit that laziness on my part contributed to the problem. As soon as I received the watch and had the crown issue, I should have escalated it with the seller immediately. I did contact the seller right away, but when he said he never had an issue with it I moved on. I was on an expat assignment out of the US at the time, so I figured it would be less of a hassle to just get it repaired locally than to push it with the seller, deal with international shipping back and forth, etc. Again, lesson learned on my part.
-- The AD was a big mall AD as you guys guessed. They sent it to what appears to be a reputable repair center. I have been in touch with the repair center recently, and they insist they wouldn't have worked on a replica. However, I think the suggestion that they just re-installed the fake crown and charged me for an OEM replacement is the most likely scenario.
-- The suggestion to pull the fake serial #'s from a replica site is a great one. I'm off to go troll through some unsavory waters now to see if I can find it...
If there is any potentially helpful/clarifying information missing from my story in this thread, please let me know. I would like this to be a clear record of the situation so that it is as helpful as possible to dummies like myself as they ease into this hobby and start buying watches!