Glad to share, been wanting to try it out!
I've been modifying my wife's glass equipment for quite a while, seems there always is something that turns a so-so tool into something great.
Your cutter is low profile which helps and seems to have a good scale to read, but like my wife's stuff, seems there is plastic or some other thing that seems cheap pr gets in the way of "perfection"
If I was without a laser, I'd probably make a new post for this glass cutter (that can be located without damaging the veneer and holds solid) and figure out a cutter. I could easily attach an Exacto knife blade but realize a roller is superior since the grain wouldn't take over the blade.
Of course it seems you have the same potential and just different, but similar, fixes for your cutter.
Either way, you are well on your goal. 👍