As mentioned I have not heard of any organized service for the High Holidays (RH & YK). They are tricky Holidays.
My suggestion would be to speak to the Cruise Director once onboard and ask to reserve a room for Services and that it should be listed on the Cruise Compass similar to the Self Led Sabbath Service on Friday nights. Every Royal ship I have been on has Siddurim (Prayer Books) either Conservative or Reform or both. You can also ask that they make Challah and supply wine, usually Manischewitz.
As to Kosher Food, the pre prepared, strictly Kosher frozen meals are available all year round and do not cost extra. Kosher for Passover meals are available with a 3 month advance notice. You get to choose your appetizer, soup, main and dessert, by coordinating with the Maitre D the night before.