Cross-Country Road Trip in a '68 Barracuda

If the weight you are adding is more in the back seat area and less towards the back bumper I think that you will be fine. With the back seat folded down that should be possible.
For suggestions, have really good / new tires on the car, with a spare, pack a 12 v tire pump. Don’t rely on the bumper jack,get a light weight nascar floor jack.
Have you and your traveling partners on different cell phone carriers to minimize dead zones. Keep the phones charged.
Welcome to Indy, that is my hometown.