Oh, forgot to mention that I also replaced the springs and poppet bearing during one of these attempts. This did not solve the problem either.
I�m not sure if the shim or the new hub assembly ultimately solved my problem. After three attempts, I was just happy to not take it all apart again. I will say�If you see the chevrons on any of the components look like mine did, replace the part.
Clearly, I�m not an expert with these transmissions or I wouldn�t have had to disassemble it three times. I take that back�I am an expert at disassembly and reassembly. Not something I wear proudly.
This is where I shimmed the case�right behind the rear bearing.

I can�t remember the full range of movement you want to see. I believe Bretto here at the 3A mentions it in his transmission repair thread. I made the shim to split the difference on his suggested range. .013 worth of front to rear movement on the shaft. To achieve this, I think I made the shim about .005 thick.

You could probably test this �movement� without taking the transmission or transfer case out.
Remove the PTO cover and main shaft gear that ties the tranny to the transfer case. Try to set a dial indicator up to read the movement. It might be a little tricky because you�re working inside the transfer case housing.
I don�t recommend it, but you might be able to shim excess movement by just removing the transfer case.
I would be happy to give you a call, but there are people here that are far smarter than I am on this transmission.
Tim