The TPS for the automatic, is actually two TPS's in a sandwich, the outer (or front) is for the tranny (TCU) and the inner is for the engine (ECU). If the high idle is caused by the TPS, it is usually a very high voltage thing, in the rear (or inner) ECU half of the TPS.
The TPS for the TCU, starts out at the index voltage (often around 3.85-4 volts or so) and the voltage goes down as the throttle is opened. For the rear or inside half of the TPS, the index voltage is low (0.6-0.8 volts or so) and gets higher as the throttle is opened. They work just the opposite of each other.
Checking the grounds for the both halves of the TPS, is a good idea. It will have a little resistance, but excessive resistance in the ground circuit, on the TCU half of TPS, will affect the initial adjustment for the other half. Cleaning the connectors is also a good idea.
If you adjust the TPS use the TPS ground, not chassis ground. There is a little built in resistance in the TPS, ground circuit (through the TCU and ECU), but it's pretty minor and at a guess is through a capacitor.
Mine works fine anywhere between 82% and 86% (for the TCU side), actually seems like it has a bit more zip at the 86% setting, which translates out to around 4 volts, like you mentioned.
You can check the inside TCU, just like you would for a stick shift. And can also check it for hitches or shorts with a needle type ohm meter pretty easily. I had one TPS, that had a dead spot in it.
You can watch the piston in the EGR work in and out, as the RPM's (vacuum) changes. You can plug the vacuum line before the transducer and try it out. If it quits and or sticks closed, chances are you won't even notice it. If it sticks open, it can make for a really poor idle and even stalling.
A sticky IAC and/or a vacuum leak will sure mess with your idle. I've had a sticky IAC and a minor vacuum leak at the same time, makes for some extreme idle changes. You can plug all the vacuum lines except the MAP and try it, just for a test or unplug them one at a time and plug the opening with your finger and see what happens. Vacuum leaks at the intake manifold gasket can be tricky to find and often change with motor temp.
I had a 1000-1500 RPM idle once, which turned out to be the vacuum line to the vacuum canister, being cut on a sharp piece of sheet metal.
I've had the IAC stick in may positions an occasional cleaning and a few drops of light oil around the piston (so it drains behind the piston a bit), seems to help. Pulling on the piston can have bad results, ask me how I know this.
