Is there really good distortion correction software?

Mike, I take it you know you can use the selection tool to select just a small area of the image and use 'Warp' on just that section alone. Done carefully, that allows continued warping without distorting other parts of the image.

You might do a little test image using actual graph paper, as mentioned previously, just to try out the system. You might put a rectangular image on a layer underneath the one on which you are working and keep the working layer somewhat transparent to match them up accurately.

Cheers, Tony.