Alrighty. I believe resolution has happened.
Along the journey, I threw some money at a couple parts that didn't help at all.
Thinking that a sensor was bad in a string of grounds. I also did a lot of swearing and wondering what could possibly be causing the problem.
In the end, Highlander gets the thanks for figuring out my problem. This past weekend we swapped his motor. Once we started the car it occaisionally hiccuped like mine. While I found this funny that my car had infected his...it told me that when either of us found the problem...the other would benefit.
I took the car on a test drive and it died. Time to find the problem.
The connector to the ICM was loose and not fully bolted up. This fixed AJ'* problem and I immediately found mine to be connected very well. Were the contacts dirty or corroded? Was the ICM bad? W/o having a way to test ICM'*, I changed mine out with one from my pile of parts. So far, no codes, not hiccups, no flashing shifter lights on the console.
I have determined that the park neutral position switch code I was getting was due to the motor actually stalling and restarting quickly enough that while driving I thought it hiccumped and in reality the PCM saw this as being started in gear. The flashing of the console lights was the PCM'* way of telling me it wasn't happy.