I find it unusual that the AD gave you a quote on service, they never do that. The answer is usually “they’ll inspect and let us know, then we’ll call you”.
I just serviced my datejust and it cost me 1100 because they replaced the crystal. All I got when it returned was a bill and a green travel pouch.
I’ve serviced watches with Rolex, AP, Vacheron and Lange and have never had any dealer “quote” me any prices. They know full well, that they don't know what's wrong with the watch until its disassembled under a microscope.
Only one of those watchmakers that gave me any type of authenticity papers is Lange, which only stated the watch was originally made by them, nothing more, nothing less.
They would never give an authenticity paper back on any watch after original point of sale, just Patek I believe offers “archive” papers similar to Lange. But Rolex doesn’t do that, let alone return a watch to a customer with an aftermarket bracelet.
If you sent that watch to them, you’re getting it back with a new factory bracelet, crystal, likely crown as well. And that isn’t 700, nor happening within 2-3 weeks. It's 6-8 if you're lucky.