ballscrew to stepper shaft alignment

[BeagleBrainz]

First off, is the undriven end of the ball screw constrained, from your photos I can not tell.

There does seem to be a large portion of the Z axis is unsupported, is there any flex/for & aft movement in the axis where the stepper motor is mounted.Could a redesign be possible to reduce the unsupported portion ?
The plate supporting the stepper seems a little on the thin side, this maybe something to look at. A little more mass and better (as good as you can get it ) alignment would be one thing I would look at.
The cheap couplers as shown in the photo are not the best choice, a Lovejoy\oldham coupler is a far superior solution, I have been using them on my mill for 5 years with no issue( tho I think they may have been in the vicinity of $80 AUD per piece ).
Be aware that some of the bearing blocks do not contain angular contact bearings but just regular roller bearings (and cheap ones at that) that are not suited to the application.
Is your ballscrew\ball nut aligned ? I mounted mine in such a way that there is some movement prior to snugging the mounts, as to allow the ballnut to find its position on the ball screw. This was due to the design of how the original lead screw & nuts were mounted. I did have an issue with the Z that required some fettling.

There could be probably a dozen more things that may be causing your vibrations.

Please note that I am playing devil's advocate.