Sounds and looks about right to me, did you get the rails and bearings from fred @ BST?

I've just been setting up a bed axis lead screw and had the same problems last week, I noticed in your video that there was quite a gap between the ball nut mount plate and the ali extrusion that passes under the machine, I'd say you need to shim that gap to perfection, just take your time and have the plate screws just finger tight so you can see any movement the plate wants to do, its likely you'll need to get down to beer/coke can thickness for shim material.

Then when it looks like you've got it close, run the gantry up and down a few times, do this with the ball screw mounts just finger tight as well so they can find their natrual sitting postion, then start at the floating end of the screw with the gantry down at that end as close as it can go (with-out falling off the rails), tighten the fixings for the ball screw mount at the floating end and then run the gantry up to the fixed end and do the same, creep up on perfect alignment and the ball screw should spin effortlessly as you move the gantry, I've got my X axis (gantry axis) so close doing it this way that i can push the whole z axis assembly from one side to the other with one finger and think that's the standard to aim for on the other axis's.

You can fine-fine tune each with a dial gauge later ;-).