WTF???
I am real confused now. P0720 is a circuit malfunction at least, not a ratio mismatch or something, so you are looking at an electrical fault of some nature and all the parts are lightweight and easy to wrestle with. I am guessing an intermittent connection or maybe the OSS is bad. Check for bad connections first, especially after all this splicing and swapping. The fact that it does it without starting the engine or moving the vehicle (turning the output shaft) tells me you probably have an open circuit, a short circuit, or an intermittent connection somewhere in the wiring to that sensor.
P0700 is the generic "something's wrong with the trans control system" so ignore that one till you have the P0720 licked. Might want to double check that your NSS is properly aligned however, though that usually causes a P0700 and a P0705. It's easy and fast though so you lose nothing by checking it.
You have had a real rough time with this one, I have never seen anyone get this unlucky with an AW4 control system.