We're plotting our trip down 95, not as far as you. though, only from NJ. Current plan is to leave Friday night for a Sunday check-in, but stopping Saturday afternoon in Jacksonville, stay there overnight and go to sleep super early, so the next morning we're rested and only a few hours away from WDW. And if we happen to make good time Saturday, bypass Jacksonville totally and see about getting a room anywhere on WDW properrty Sat night and then check into our actual resort Sunday.
You might find, if you can do it that the Jacksonville plan might work better. Start driving late Saturday afternoon or early Saturday evening, you could possibly be halfway down by breakfast time. Then drive as much as you can until early afternoon, get a room Sunday night with the intention of getting to bed no later than 8 or 9 to sleep off the long drive prior, then the next morning, you're pretty close.
Another thought, if you left home in the wee hours Saturday night/Sunday morning, you could drive to Lorton VA and take the Amtrak AutoTrain to Sanford Fl. Your car comes with you (though you're not in it once you're on the train, it's in storage), round trip in coach seats and AAA discount (you've got AAA, right) would be $1100, $586 if you just want to use it to go South and then drive home, and each trip includes dinner and a continental breakfast. Maybe not as cheap as driving all the way down, but deduct $120-150 for the fuel you don't consume, $200-300 for the hotel rooms you don't rent (assuming you'd , and even if you picked up fast food for dinner and bagels and juice for breakfast, that's about 4 bucks right there. And someone's doing about half of the driving for you, giving you the night to sleep off the early morning rising you did to start the drive.