@ that the map image is a perfect rectangle.

Usually all map is a perfect rectangle if use the right projection.

@ In my Google Earth trial I have some joints where a "gap" of up to 3 pixels appears when viewed in GE.
Maybe my border cropping is not accurate?

It is normally for quick work. No doubt it give the error but on this scale this error is a negligible for practice. Errors in GPS position and map are more significant. You can play with calibration again and again to see the perfect merging but it be waste time. Try to get some tracks from open source and put it on your map - it is more reliable for map verification.