JP, I wouldn't be afraid to do it with my truck. I have experience towing and my trucks engine/tranny have been freshened up and the brakes upgraded at all 4 wheels.

Towing across most of your route should be fairly flat for the most part. I am not sure where you will encounter the mountains, that will be an issue.

Stopping should be your biggest concern. You will have to stop both the truck and the car with the trucks drum brakes. IMHO

John