We too are usually January travelers. I will book our main park in Florida in advance, knowing that I will likely arrive in Florida ahead of schedule. For those days I arrive ahead of our reservations, I wait until I get the latest weather forecast for the areas I will be traveling through, then I call a place(s) for a short term stay just as we are leaving. Usually, no trouble getting a short term (a few days) spot north of I4.
Note that we have had to change departure dates a couple of times due to weather along our route, so your idea of planning for this is a good idea.