So you installed a reman transmission?? Or did I read that wrong...
Sounds like you found the problem... clutch stuff. I found that the center hub isn't tough on many clutches, including the OEM pieces... the one we removed from dad's truck at 220k (original clutch) had every spring in the hub loose... however, the flywheel was in top shape and we didn't even resurface it... the replacement clutch was a "stocker" SBC... I'm glad to see they treat their customers well.
Mine was replaced under warranty when new for a defective disc... when I saw you had an 03, that was one of my first thoughts (it only applied to the 03s for whatever reason, but it afflicted my 04. 5)...
I will watch this thread intently as I am really interested in what you might find...
steved