We did this just about three years ago, moved from Bakersfield California to East Tennessee about 2300 miles. We had three indoor only silver Persians and one inside/outside Formerly stray cat. And a Yorkie.
I think my husband figured out the best scenario ever for moving kitties. We got a cab over camper and he drove the truck and I drove a car. The kid hes got to stay in the cabin over the whole time, no concerns about sticking them in carriers or moving them in and out of hotel rooms. They had a litter box, food and water always available. They got to sleep on the queen bed in the cab over and watched the miles go by.
There was only one hitch, and that was when the heater quit working in the cab over. We moved in January. Luckily hubby is handy and got it working. But we were fixin to put them in their carriers and bring them into the hotel for the night if it didnt. (Notice the east Tennessee lingo :-)
We had bought a used lance just for the trip. We kept it, thinking we might want to go camping eventually. Or if we decide to go sightseeing and dont find a good pet sitter. The cats didnt seem stressed at all and our worries about them were minimal. They didnt even try to escape when we opened the door, although we were careful just in case. But we have Persians, and they are pretty mellow and low-key. But even the tuxcedo cat seemed happy where he was.
The camper idea is excellent.