Very insightful post! One of the biggest take-aways, for me personally, was how you laid out level progression as it related to narrative. Linear puzzle progression does lend itself well to a narrative driven game. Great point that I never really thought about before.
Regarding the N-Gon idea, I love it! It's a really good idea and will be a nice reward after each level. It could be a good opportunity for some juicy animation too (maybe not mobile-game levels of juice, but something fun and exciting).
Out of curiosity, do you plan on having the N-Gon amount rewarded at the end of each level be variable, for instance if you beat the level in fewer moves you get a higher reward? I know there is some debate about "move counters" in puzzle games and how they can detract from the point of the game. I'm curious if you've thought about this for IGEO though.
Thanks again for the post, looking forward to more!