Issues with my 2001 F-250 7.3L transmission continue...

I know you said it is an 01, but double check the off chance and see if the transmission cooling lines have the pass through in the bottom of the radiator. For a short time Ford decided to delete this and rely strictly on the oil air heat exchanger, which does not work well when going slow pulling a hill or backing up! I believe in mid 2000 model year they reverted back, but it is worth a quick look. If you do not have the pass through, you will need a radiator for a later year that has the pass through.