I did find a copy of the 6HP manual and I'm not convinced it is the transmission itself.

I have been able to reproduce the symptoms in this video:
https://www.youtube.com/watch?v=PBoAdbyN23U

Especially in terms of turning the wheel and there being no movement and having movement forward and back if the wheel is straight.

Actually, you can have movement forward and back up to 90 degrees left or right on the steering wheel - but that would be maybe 15 degrees of deflection on the wheels, not enough to turn a corner certainly. What happens over 90 degrees is that no power reaches the wheels.

So this tells me a few things:
- Possibly there is no power going to the rear wheels
- If there is power going to the front wheels, it gets cut off once the steering wheel turns past 90 degrees left or right from center.
- It makes no noise going into gear - nor does it make any noise going into neutral or noise from neutral to park. only when going from R/D to P.
- And another reason why I don't think it's the transmission itself - it engages and does send power properly both forward and backwards (R/D). Which means there is power going from the transmission to the transfer case at least just to deliver it to the differentials either front or rear.