My take on what I have read!
The movement you have shown in all three videos, I would expect if the steppers were not energized!
So that side of it all looks good to me.
The oval shape that you seem to be achieving, I suspect it is caused by the fact that your “better Z middle” is slightly longer then it should be.
By longer, I mean that your X and Y rail will be pushed out of square, in the quadrant of the Z assembly, I’m guessing by 1 to 2 degrees!
To check this I would move the tool over the same position where you cut that circle/oval. From both ends of the X rail, and on the same side of the
X rail drop a plumb bob down to your work surface/table. Mark the two points on this surface and draw a straight line between these two points.
Now do the exact same thing on the Y rail. Take a square and check where the lines intersect, are they square?