Contrary to what I expected, LightBurn doesn’t go through the image in a consistent direction, but it does draw most of the patterns while traveling along the X axis.
What’s significant:
- Very few of the six-point shapes are misaligned in the Y direction and those few aren’t off by much
- The three-point shapes generally have a single misalignment at the far left or right end of a line, then the rest are consistent
Scrubbing through the Preview suggests the misalignments happen when the head moves to a new row and starts drawing a three-point shape.
Except for that one screw you can’t see, let alone reach, in the Y axis drive train. 
I think there’s a pulley or coupler secured to a shaft with a setscrew resting on a flat, but the setscrew is slightly loose and allows the flat to jam in one of two fixed positions. It will feel tight when it’s jammed, but the force required to move the heavy gantry is enough to dislodge the screw from the flat and rotate the shaft to the other position.
A previous thread with pictures of what to inspect inside the cabinet:
At this point, I’d loosen every setscrew, one at a time, along the way from the motor to the gantry (both left and right), then rotate the shaft / pulley / coupler back and forth while tightening that setscrew. That will let you feel the motion as the setscrew bites into the shaft, so it will end up nice and tight in the middle of the flat.
That you will find it essentially impossible to get enough hands and eyes into the places where you must tighten and wiggle goes without saying …