Paul -
In the squeaking sound video, is the machine running in delicate?
I have heard similar sounds a couple times, I hope I'm wrong but it sounds like dry bearings. What happened to me a few times a while back, several installs and take-aparts allowed turbine oil in the bearings to drip out, leaving them dry, or almost so. I have noticed this too in a couple machines that have been sitting long term. The turbine oil slowly but surely over time made it past the seals, leaving the bearings dry and the basket brake pad all wet.
A quick way to find out if this is happening or not is to remove the agitator after a full spin - if the basket lock nut is uncomfortably hot, the upper bearing needs more oil. There will be some warmth there of course with tight bearings, but if you'd burn your palm, its too hot. If you remove the basket you can check the lower centerpost area as well. Same deal with that one. Unless you are sure there was lots of turbine oil in there, I'd direct my attention in that direction.
I hope there is another answer, as otherwise you'll have to remove the transmission and spin tube yet AGAIN....
Gordon