We have a 21 hour drive to the Fort and usually do our relatively short "nap time" in Walmart parking lots. Walmart allows this in many parts of the country although the counties in/around WDW have an ordinance against it (I also think that it's forbidden in the county Daytona is located in??) They are well lit, security patrols them, and you'll generally find a few other campers there as well. Just park out in the outlying areas of the lot, out of the way of the regular shoppers. The upside is that is you need anything, lots of these are super centers and open 24 hours. We've done this many times now, and have never had any problems.
We tried truck stops a few times, but they were VERY noisy, not always very well lit, and some of them were kind of... sketchy.
Neither option gives you power or water. We only use power for the lights, so the batteries take care of that, and I bring a few gallons of water with us for drinking, washing and flushing (unscented baby wipes are also good for quick clean ups). Our camper's heater runs off propane, so we've never had a problem needing to turn the heat on if it's chilly and we frequently do, as we usually go to FW in Dec and are traveling to/from NH.
Our itinerary goes like this...
Leave NH about 5pm
Drive to approx. Richmond (couple of Walmarts there right off 95) and stop at Walmart around 1-2am-ish. Sleep until 7-8am.
Continue south - get to Jacksonville FL around 8-9pm, stop at Walmart. Eat and do our grocery shopping for our stay (easier than doing it when we get there), sleep until about 7-8am.
Continue onto Ft. Wilderness - arriving usually by 11am.
We have a hybrid TT, but instead of putting the ends out for these quick overnights, we just make the bed on the sofa/dinette before we leave, so it's all ready to hop in when we park. Being in a 5th wheel, you'll be all setup anyway.
Good luck and have a wonderful trip!
PS - Just wanted to add that if you go the Walmart route, you might want to map out where they will be along your way so you don't have to go hunting for them. I think Walmart actually publishes a book themselves for this, and there are other RV books that give you lists of what's off the exits on major highways around the country (just make sure you get the most current version)