I've replaced my TPS and reset timing to 3 degrees BTDC and all is good with the world.
The TPS originally on the car when I got it had a "flat spot" per one of the dealer service receipts. I replaced it with a (claimed) known good one from eBay from Japan. That one was on when I started this thread with the undesired behaviors. Then today, I replaced the TPS with a brand new one from a Toyota dealer.
It is now accelerating smoothly, and doesn't have any doggy-ness, or lag across the acceleration curve.
It is shocking how much impact this silly sensor can have on the way the engine runs.