How much tension is it under when tight.?
How are you aligning the screw with nut.?
Have you checked there's no play or slop in the rotating ballnut.?

When leaving the one end lose does it work ok without holding it and if so does the screws lose end move up or down when Z axis travels along it length.?

I see in the video with you holding the end that the screw is a sloppy fit where pass's thru the gantry sides. Is this correct or have you removed a bush or anything.?

Really would think that if you nipped the screw up at each end just enough so the screw can slide slightly then move the Z axis to each end a few times it will align it's self then tighten the ends.