Then you will need to talk to the Purser's office on the last day of the cruise and SHOW them the airline reservations.. and demand that you get FIRST OFF the boat luggage tags and departure passes (or whatever the line will call them).
The cruise line will know ITS passengers and what flights they have to make. They will group people by that time frame... say White tags are first off, Green are next (maybe 10 minutes later) ... all the way to say Purple who are spending the night in town and have no rush to get off the ship.
Since it sounds like you made th flights yourself.. the cruise line will not know your requirements .. and give you middle-of-departure tags typically. You HAVE TO get these changed .. check with the Purser early .. and often about getting the FIRST group off tags.
THEN when you get off the ship.. consider grabbing (and paying$$) a porter to get all your luggage together and GET OUT to a cab. A porter normally will jump into the lines and also be better off in getting you a cab (knowing where to go). If you have paid for transfers with the cruise line .. and are not 'legal' they won't do anything. Take a CAB and tell him/her to RUSH ...
Seriously tho .. have a backup plan. Know the NEXT flight after this one in case you miss it .. and then hope the airline can/will accomodate you.
NOTE on the morning of arrivals .. there typically is no room service and the sit-down restaurant and buffet are open. Get up EARLY and go to the buffet restaurant and be ALL READY to go at least by 7:30 .. sitting in the lobby (or where ever they tell you). Don't dawdle... you are on a mission!