I’d bet you the rear U joint is dry and eating itself.
Note how the shaft goes off center and then straightens up when spun faster.
Not feeling play in that U joint doesn’t mean it’s good.
They can be tight because the grease is all gone and it’s binding.
As usual, someone else beat me to it. I had almost the exact same thing several years ago. After throwing money at several other things, It wound up being the rear U-Joint. The U-Joints were fairly new, so it couldn't be that, right?
