Welcome to the world of old truck bodies. There is usually nothing that is as abused as old trucks. For decades people throw things in the bed, slam stuff down on the bed sides and tail gate, and generally don't give a rats' @$$. Then one day someone wants to make a nice rod or custom out of it!

First I would see how much of it really shows when the bed is in place. That way you can decide how straight it needs to be.