The crowd issue for Grand Cayman comes into play when the ships arrive when they are not expected. (Like when they change itineraries for a huricane) Grand Cayman provides their own tenders (Princess uses their own tenders too). If the 7 ships are planned on, then the island tenders are able to handle the load if not, then the port will let the ships use their own tenders too.
If you need to be off early, make sure you follow the proceedures called for "those with early tours" You will get on the first tenders.
Even if you booked your own tours, don't listen to them if they say "if you booked a tour on the ship".. just go where they say and tell them you have an early tour and need to get off.
It should not be a real big problem.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013