When my Rolex needed its 5-yr "tune up", I sent it back to the place I purchased it from--an excellent reliable Rolex reseller. What a set of instructions they sent me first--"go to UPS and get 2 blah blah size envelopes and a blah blah size box and get bubble wrap and wrap the bracelet this way and tape this label on it and then put it in envelope #1 and then tape another label on it and then put it in envelope #2 and tape another label on THAT envelope and then put it in the box ..." the instructions were very detailed and long but the watch got there next morning and I had it back in something like 10 days, and this was for an entire tune up, but I had nothing broken to fix (did get another link added).
Your watch has more mechanicals involved with moon phase, etc. but still that was an outrageous amount of money, imo. But putting the band on wrong? Not acceptable!
I feel lucky that I found a great place to purchase & service my watch (did tons of research first); one of the authorized Rolex dealers close to me got busted a while back because the SAs were purchasing all the Rolexes when the shipments arrived and jacking up the prices and selling them privately--I would never leave my watch with them.
At the end of the day you got your lovely watch back safe and sound!