honestly, it sounds like a BMW I worked on a couple months ago, only his power would cut at 6k instead of 3.
Take some carb clean and clean out your MAP.. we ended up having to replace his, but cleaning it out did help too...
TPS looked fine from what I watched if it was on the left... that's what I'm guessing at least. there were random times when your map would peg out, and it's not supposed to ever see full voltage.
When it see's full voltage, it sees either a lot of air in the manifold, or no air in the manifold. I'm guessing it's no air, because then it cuts fuel to compensate and thats why your engine is staying there.
If you can check our o2 sensors, try looking at what happens with that around 3k when it cuts. if SHOULD keep switching, but if you're not getting any fuel it'll flat line.
