I would not worry about trying to turn the long shaft.
If you can turn the small shaft one way by hand and watch the long shaft agitate back and forth (it will be slow moving) it should be ok.
Turn the short shaft by hand the opposite way and you should be able to see the part at the bottom of the long shaft that the clutch mounts to spin in one direction too.
I would guess all you may need is a new coupler and there was no reason to even remove the transmission from the washer in the first place.
The coupler is a common part to wear out and I must have replaced hundreds or more of them over the years. It's a cheap and easy part to replace.