As to your vibration; I know youre working hard at it. And youre pretty sure its in the trans. And it may well be a contributor.But Id like to relate something that I think might apply.
Years ago, I was chasing an annoying vibration too.In my research, I came across an article that said something like this;Every spinning component in that driveline has a natural frequency at which it wants to vibrate. Some like to add up to others. Some cancel others. The article went on to say that each member in the drivetrain could be well balanced, yet when together, could vibrate. It went on to say that there were 3 major contributors; powertrain,wheels, and body.
Since your combo vibrates when stopped, you can pretty much rule out body.
Since it vibrates with the wheels off, thats out.
Since youve tried it with out axles,third member, etc,youve pretty much ruled everything out, except the trans, and the combination of engine/trans. Good work BTW.
So, at this point, I would suggest bolting on a proper balance flywheel and bell house, to eliminate the engine once and for almost all. I suggest this for three reasons. #1)the 727 is down and the 904 is kaput, and 2) if the engine isnt the source, then,the tranny has to be, and 3) its extremely rare that the automatic would be the source, although I can easily imagine internal situations that could be contributing.
If you cant find a correct balance flywheel, I myself can imagine a way of bolting on a neutral balance flywheel, and that flexplate behind it. Get creative, I am sure you can figure out a way.
Anyway, this late in the day, youve probably already bolted that 904 on, and are nearly ready to post results.