Zee flyboy,
I appreciate your input. Here my thinking.

If you push on spindle, the axis shafts flex. The pivot point is the ball screw, top rod flexes forward, bottom rod flexes back. Vice versa if you pull on spindle.

During this motion, the gantry stays stationary.
The backplate is attached to gantry.

Imagine the gantry didn't need to move left/right on x axis. If I placed a piece of metal from top of z axis to backplate and bottom of z axis to backplate- it would support the spindle and it wouldn't flex. Assuming of course back plate was rigid.

To allow x as is movement- Ill use wheels on the supports.

It'll work.