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10 hours a day isn't too much to do in a day, but it is up near the most we'd recommend. Especially when you factor in camping, that will require a little more time to get to a site, and set-up and tear down, when compared to motel travel.

600 miles is about the farthest you can get in 10 hours, so I would consider scaling back days 2-4 just a little bit, and planning to go a little farther on your last two days. That will even things out a bit, plus, it could give you a chance to see a few more things that are farther from your new home - as you get towards the Florida, you can skip some things and make plans to see them again at a later date.