Don’t take the Interstate or any limited-access road, stick to less-trafficked roads that go through actual towns. Carry tools and spare parts. I have an ‘87 Toyota pickup, carry a complete set of parts that I can replace easily on the road, the tools necessary. I don’t care for the Interstate, take back roads. I have also lived out of it so have camping gear and a few days’ food. I’d take the trip on my conditions.
I think the interstate would be fine, but let it run a bit at local speeds before turning off the engine, or leave the engine running while refueling, if the knowledgeable people agree.
I wouldn’t leave the engine running while fueling, but I would use the interstates because there is likely to be cell phone service along the interstates. Just slow down to 55 about three miles before your gas stop. That really is only to keep the oil temperature down after shut off.
Much of the problem with limited access roads is room to work on the car on the shoulder. A few years ago, a man was driving his Model A on I-70 in MD when he had a breakdown. While he was working on it, he was struck and killed. The shoulder is fairly wide on that stretch of I-70, but I don’t know how close to the highway he parked. Also in your favor is that it’s likely that other drivers have to slow way under the speed limit if they stay in the lane closest to you or move over a lane when they pass you.
They may even stop. I do. It’s harder to do on the Interstate. I also may turn around and come back, much harder to do on the Interstate. The drivers are more likely to be local.