Interesting, thanks for the additional photos.
Your main issue seems to be only really be showing at the rotary (the skipped lines), which appear to be regular despite changing line interval or scan angle - is the interval of the problem the same as gear gogs/belt teeth at the rotary?
The other pic (IMG_1669) on the flat with the ‘boxes not square’ and where you labelled the ‘Box is wavy’, is possible a secondary or downstream issue since it also seems to appear at the rotary (IMG_1664), so you may want to check the laser module - mount/head assembly/optics, for any looseness that might contribute to a front-back wobble.
It might be useful if you ran this backlash test program (on the flat):
Backlash.lbrn2 (73.5 KB)
Post the results here please.
Check for the hallmarks of a sloppy Y-axis.