According to the price list here:
https://www.sinn.de/en/Customer_Service.htm
It looks as though the base price would be €415 for a service:
Standard Overhaul Services
– Factory overhaul (disassembling, cleaning, lubricating, assembling and adjusting of the movement, replacing of all
technically required parts)
– Renewing of the seal system (all seal rings incl. the crown, push-piece only if technically required)
– Cleaning of the case
– Cleaning and checking of the metal bracelet
– Repairing of the metal bracelet (if necessary and possible, excl. clasp replacement)
– Final inspection
plus €200 if a case refinish is required. Return postage will be a bit extra.
They always quote the above as a guideline in case of further work being required.
Can't help with sending the watch as I was lucky enough to be over there and dropped my U1 off in person. They sent the watch back via UPS.
I was far more comfortable having Sinn dealing with the watch directly rather than paying a UK based middle man..... Very happy with the service (although 3 months turn around), give the service centre a call, they're very helpful.
Good luck with the service!