Your Z axis is binding. (I think)
A few things to look at.
-The Z rails can touch ( and should) but not stick. so if you a cocked just a bit they will grab and bind. This is just a friction thing. For safety do your tests at the stop block so you know the machine is “straight”.
-Both sides. I would start all test (and cuts) from zero. Meaning both XZ mains should be resting on the rollers. Kinda the same as above, you get it crooked and it will bind (and break parts). So always, no matter what start from Zero so both sides are level, then move up and down. Most LowRider’s will not stay in the air unless they are binding. That is actually how it got its name, power it off and it looked like the hydraulics on a lowrider lowering the car. Original name was “full Sheeter” or something like that.
-Where I actually see a bigger issue. What is up with your coupler? That things should be straight and smooth, Is the leadscrew straight and super easy to move by hand up and down on both sides?
What I am seeing is it is moving one direction, down, but binding the other and slipping, down. I have some videos of the previous version with a bunch of weights on each side, the steppers have no issue moving, unless the nut/screw combo in binding. Make sure it is free and smooth, lubed and it should be fine.