The difference between frames is due to the year difference. 60-62 had a wider frame than 63-66. That affects not only the center cross sills but also the rear sill as the mounting brackets on the rear will will not line up with the frame rails. Of course the wood bed to frame holes will not line up either. The wood boards are the same width for both series, but the mounting holes are placed differently for the two types of frames.
Otherwise the beds are about the same. The swap should not be too much trouble, especially with new sills and new wood.
Mar-Ktech