That range of a jump sounds like the transmission "riding the clutch." I've noticed the truck do this on highways instead of downshifting.
A few weeks ago, I had a similar experience while I was towing a trailer and Tow/Haul was engaged. The transmission is not supposed to do this while towing but it was anyway. In fact, RPMs were jumping wildly while going uphill as it disegaged and reengaged the torque converter. However, this was not a transmission problem, nor do I think your problem is.
I know very little about how our transmissions work, but I think I can point you in the right direction. I'm pretty sure the transmission is controlled by the computer, not a separate controller somewhere. See if you can locate one for a good price. I was able to find it on rockauto.com for $168, with a $75 refund for the core. Probably the best price you'll find on these. But you probably want to verify some of this first. I'm no expert on trannies, this is just my opinion.
