I vote day before too.
Years ago (when we lived up north) we were doing a family NYE cruise out of Miami. I worried about snowstorms at that time of year, but it was FOG that blanketed the entire area that cancelled our Delta flight out. I never considered fog, but should have guessed there would be a problem when we couldn't see much out of the parking shuttle's windows on the way to the terminal.
Thankfully we had booked a day before package with the cruise line, so we all piled back in our cars and started down I 75. Delta helped us by advising the airports all the way down, but if we had to drive all the way to Miami we would. When we hit Lexington it finally started to rain and voila - fog lifted.
We ran in the Lexington airport and checked at the Delta desk, and yep, they were aware of us and could offer us seats on a midnight flight, so we grabbed them.
I think we finally hit the day before Miami hotel around 3AM or later, but hey, at least we were able to make the cruise. Of course, flying home we had to return to Lexington and make the long drive back home, but we had made our cruise.
Compare this to our friends who were also at the first airport (but sailing on a different cruise) and who didn't book the day before or have trip insurance. No way they could make it down in time to sail that day. And they hadn't booked the cruise lines air, so they had to pay for flights to the first port to join their ship in mid cruise - which was in
Cozumel, 3 days later. All that money, for essentially a few days on the ship, but they were bound and determined to take their cruise and at least not lose that $$.
I guess once something like this happens to you, you will always go a day early from then on LOL.