Mine also idles a ton better with the TPS unplugged, but I did not try to drive it. The TPS is pretty new, I think I got it in April. I put the old one on and it does the same thing.
might also be the 'pigtail' that connects to the TPS. Mine had similar symptoms. Ended up that one of the wires right off the connector was faulty. The dealer swapped in the new pigtail and it was fixed.
Oh... and make sure you reset the computer after trying each of your attempts. Though you'll probably have similar symptoms to what you're currently experiencing until the computer relearns.
