I'm with the others, I-75 is your only real option if you want to avoid mountains.
As for your timing however, I strongly suggest you reconsider your departure timing. I've done that trip more times than I care to remember and the few times I had to leave late in the day during cold weather it turned into a fiasco.
Unless you get super lucky with the weather you are going to have a pretty frosty sleep that first day. It looks like you will still be quite a ways north and from your comment about just stopping when tired you will be dry camping and so will be maxing out your batteries and propane trying to stay warm.
This is a BIG part of the reason I have a motorhome, I can keep the whole unit pretty warm while driving down the highway without using up any propane. This means when I stop the unit is already warm and takes a lot less energy to just keep it warm compared to having to heat it up first, then keep it warm after that.
If you're able to leave early in the morning and drive for 14hours the first day, plus stops, so 16 to 18 hours on the road you would be far enough south you'd be past the worst of the weather.
This brings me to my final point, the weather itself, if you leave later that night that time of year you run the risk of driving through some pretty nasty weather in the dark. This brings me to my final point, the weather itself, if you leave later that night that time of year you run the risk of driving through some pretty nasty weather in the dark. This never a good thing and certainly not a great way to start a vacation.
