I am retired Military and I book thru, interliner.com, because they speciallize in Airline employees and as well as active duty and retired military. I due all my booking with the five girls who have given me excellelt service for several years now.
Mariner of the Sea, which is the same class as the Navigator of the Sea have seperate men and lidies steam and sauna facilities right by the gym. In the afternoons I always exchange my room card for a locker key and have a steam, sauna, shower and shave in this space.
Hope that answers your questions.
Last time I looked the price for an inside cabin for this transatlantic was in the neighborhood of $950 for an inside PR