To be honest if you can't fly with them, then the next best thing would be to hire a car for a one way trip.
Most major car hire firms will allow you to collect a car from one location, and return it to a different one.
Having a car means you can set your own agenda, and carry all the necessary items for a few days.
A shower curtain, fleece blanket and a few cable tied C&C grids would make a perfect temporary pen in a hotel/motel when you stop off overnight.
It will also give them a break from the carriers, and if you stop for a picnic en-route you could even take them out and let them have some fresh air if you come across an appropriate quite place off the beaten track.
Do not use a pet transport service ever - they have very limited expereince with anything other than dogs or cats, and are not a good choice for anyting more 'exotic'.
Pick the right time of year, plan your route well, and look at it as a small road trip adventure.