First off yes they need all FAs to board per the FAA. One FA per 50 passengers at max capacity is the rule for all aircraft. Even if there's only a single seat sold. (with the exception of small aircraft where flight deck doors aren't secured and the FO is usually your FA as well)

It is a delay, considered controllable due to crew issues. Yes, it's the FA's and ultimately the airline's fault but not IDB. They reaccomodated you getting you to your destination on a direct flight two hours later. If only all delays and reroutes could be this close.

Try a friendly face to face explanation at the hotel... maybe you can get credit there. The hotel is your host... that number you called may have just been some booking agent following set rules. Don't be afraid to pour it on how happy you are with the hotel.

And by the way you're the envy of many of us not in Jamaica!