Truck looks pretty nice. You may want to try to super tune the 350 to give it a chance before you pull it. Also some flow-thru mufflers and even headers would make a difference. I have a newer 350 in my '72 C-30. It's not registered and I haven't had it out on the open road yet, but it seems like it will be plenty good enough. Do you have a 2-Speed Rear in it?
The truck chassis might be a little short to haul a car on it as it is, but would be a good goose-neck truck or as a traditional puller. The bed size will depend on the length. What is the CA? (Cab to Axel measurement).
Welcome to the site, by the way.
Bill