That's why I thought it was an intake problem or an intake leak - the hard shifting is part of a "safe mode" that the computer goes into when the MAF is disconnected or there is a vacuum leak. My '00 Yukon did the exact same thing when I installed an AEM Brute Force on it but forgot to plug the MAF sensor harness back in. If there is un-metered air getting into the motor, the computer flips out and maxes out the line pressure resulting in crazy shifts (I didn't have the stablitrak off/traction control issues on that truck because the 2000's didn't have either system...but I'm sure that it's all part of a cascading system shutdown to prevent engine/trans damage when something isn't working correctly).
So, based on that experience, naturally I thought that the whole thing was caused by the intake tube popping off and causing a massive vacuum problem. When the issues came back even with the intake put back on correctly, it threw me for a loop. If polishing up the battery/fuse connections really does do the trick, I haven't a clue as to why. The whole thing starts with the airaid tube popping loose, and is fixed by messing with the battery cables? It's a strange problem, to say the least. Great to hear you've gone so long without having an issue though, that is really good news.
Gotta love computer controlled trucks.
ETA: Might be selling my Airaid and shelling out the dough for a Volant. Sheesh.