How to set home position for laser module very precisely - and keep this home position for subsequent jobs

While complicated, it would resolve your issue.

I would suggest just editing the gcode instead of messing with Luban files, however. If you use the laser method to line it up, you could find your repeatable origin, then use the follow code to repeat your position after writing it down on the set work origin screen;

G0 X# Y#
G54
G92 X0 Y0

You could also always write down the location and move to that each time, but depends on the level of automation you want.