Pay to go online to check flights while at sea. Also have your cell phone ready and telephone AA the minute you can do so while still on the ship (make sure the ship's cell repeater tower is turned off). You may get lucky.

Also even though you will likely have a heap of luggage, if you can self disembark and get off the ship ahead of the mobs, you may catch a break for an earlier flight thanks to that access to AA via phone and internet.

If you are willing to hustle, you may catch a break and get home a bit early.