Is there any way to book dining reservations in the Olympic dining room in advance of the cruise date

Not that I am aware of. You will have the popportuntiy to make reservations oce you board the ship. I would certainly recommend it for one evening, and then it you really like it, make more.

Tom

FWIW, I doubt you will have a problem getting a table when you want it, especially if you book promptly upon boarding. The night we were there, the room was only about 1/2 full.
It was very good. Enjoy!

If you have sailed Century before you join the Captain's Club. The take reservations prior to sailing time.