If you have time and a little money you might rent a motor home
which gives you and your cats a home-like environment and you can travel
at a leisurely pace and "discover America" while you're at it. Just make
sure the cats are not going to get out and get lost. Cat security comes
first,... and don't let them drive when traffic is bad. They hate that.
==============
I am reminded of "The Cat Who...." mysteries....

Seriously, driving might be an option, if you can plan your route through
motels that allow pets.

Jeanne