I ended up solving this using Python using basically the same approach you used. https://github.com/brockbrownwork/greek_computer/blob/main/greek_computer.ipynb

I didn't realize that you could take the puzzle apart; I just transcribed each layer using speech to text and looking through the little holes lol. I am definitely curious though how you can solve this without brute force, or at least with fewer combinations, would like to try again later. Maybe a breadth first search approach would work better, i.e.: avoiding all paths where the sum is more than 42?

Very cool Christopher. Interesting approach and nice use of WL functions such as AssociationThread and patterns. On the website it has a difficulty of 5, I wonder the average time it takes to solve manually.