Not to get too deep in the weeds on this, please understand the length of validity rule is set by each country visited, not RCL. RCL will suggest the passports have 6 months validity as that is what most countries will require. That said, it's not like they are checking your passport at each island.
Also, RCL doesn't require passports on closed loop itineraries (depart and return to same port) but do require passports for open loop, like this itinerary will be. I suggest you call RCL, or better yet email so you have written proof, to confirm what they will require.