I dive a lot with Red Sail, and have not encountered many cruise ship passengers, so you may be right about the separate boat. They also have large boats which never seem to get crowded regardless of how many are on board and provide a lot of room to maneuver when setting up equipment. Then again I dive with LTD, Indigo, and Neptune's and don't recall many cruisers, and their small boats are never very crowded either. I suppose as long as the dive op limits the number of divers based on boat size, you will have plenty of room - and all the ops I've gone with seem to do this.
I just checked on the Cruise Critic forum and, FWIW, the ops that get recommended the most for cruise ship divers are Cayman Turtle Divers, Don Fosters, and Eden Rock Dive Center