It's less than ideal. I would definitely change to a later flight. After a fun relaxing cruise why end it with a stressful situation. You could end up with a really crappy flight.
Welcome to CC. If you click on "Forums" at the top left of the page and scroll down to the Ports of Call section you will find specific forums for those countries that are full of good info for you to research.
I haven't been there personally but you may find some useful info on the Jamaica forum. Here is the link for you.
https://boards.cruisecritic.com/forum/67-jamaica/
It could be software issues, hardware issues, less than competent I.T. techs or any combination of those factors. Only they would be able to tell you.
Personally, I haven't noticed constant issues as you reported.
I was just looking at that myself. Google Maps says it's almost 1600 miles, about a 23 hour drive. For me the last thing I would want to do after a nice relaxing cruise would be to get in a cramped vehicle and drive for a couple of days.
Recommend you ask/research on the East Coast Departures forum. Lots of good info there. Link:
https://boards.cruisecritic.com/forum/317-east-coast-departures/