with that base you can also select a horizontal edge > loop > ring > straighten horizontally, then select an vertical edge > loop > ring > straighten vertically
Headus UV has a rectilinear relax feature for this. Also, Max has the straighten selection and unfold strip from loop features. But really, the results will vary greatly depending on how far the edges deviate from the original relaxed shell. If this is for in-game purposes then it's only really the UV shell border edges…