It sounds like an ECU problem. I would suggest the following, which I did on a VW which behaved similarly.
Start with engine idling, in first, and progressively shift up (use hills, whatever) to 30 MPH. At that point the cruise control will work. Engage, and use the increase speed button to establish operation at a speed which is above idle.
If that works, then things point back to the TPS, and since you have eliminated the TPS, the ECU's ability to process the TPS (digital) signal, or the ECU's interface to the TPS, or wiring.
Using the cruise control you can establish that the ECU can command the engine to more than just idle power, and you incorporate the speed sensor, etc.
As a side note, this technique was used to transport the car several hundred miles on interstates, until a repair could be done, so it is an effective get home strategy with a failed TPS.
Addendum #1: I would suggest that you try running your car without the TPS. Specifically use the technique I outlined. (It is easier with a TDI, however.) Get your car up to 30 MPH by shifting through the gears with the engine idling. Then engage the cruise control. Use the up speed button to control an increase in speed. The brake pedal will disengage the cruise, as usual. If the cruise control effectively controls the engine, then your faults point to the TPS. Having said that, the TPS wiring might be intermittent or the TPS interface in the ECU might be intermittent. Hopefully this helps you further diagnose things.