Wow, I solved this by misclicking and noticing it made a save. This was fun! Despite all the 109 variations I had, I felt optimizing was a natural progression.
I think this is a very interesting set up. I had troubles to even come ''close''. Then I kept discovering 111s, a whole bunch of those. :))
Found a 109, later, which is very nice. Will keep looking for 107, in hopes to get it.
EDIT: Eureka moment came only an hour later.
It's a great puzzle!