Flying first class won't matter. We have flown direct to Orlando from PHX many times. One time we were diverted to Dallas to refuel because of the heat and we once had a 4 hour delay that departed PHX when we were supposed to land in Orlando. Most recently, our upcoming direct flight in October was cancelled and we are now flying through Austin.
That being said, with the exception of West coast cruises, every time we have cruised out of Florida or Europe, we have flown in 2 nights before the cruise. That allows for delays as well as getting used to time changes. We usually find something fun to do the the day before we embark the ship.
Good luck, flying has become a real pain as of late!