You can rent as they will use the address on your UK licence.
I was going to mention buying a 2nd hand car, but it is dicey incase you end up with a lemon that could cost you more in money and time in the long run if is breaks down. Do your sums re a one way rental, and compare against what you would pay for a newish second hand car, especially if this your move out here, and not a reccie. If a reccie, you have to get rid of the car after, so it will be at car yard prices, which may not be the best.
Alternative is to rent a motorhome, so no need to bother with looking for accommodation other than at van parks, which may be easier than finding a hotel/motel with vacancies. That way, you can stop when you want to, leave when you want to, and no worrying about booking accommodation ahead.