Cool stuff. I'm disappointed to see that none of philosopher Dan Dennett's recent work [1] on this topic has come into these pages though. There's some overlap especially in the "thought experiment" realm, and it gets a rigorous philosophical treatment which for some is the key to this kind of problem-solving. (disclaimer: I was in the cohort of undergrads that Dennett used to review his chapters).

1: https://www.amazon.com/Intuition-Pumps-Other-Tools-Thinking/...

I recently read "Intuition Pumps And Other Tools For Thinking" by Dennett (http://www.amazon.com/Intuition-Pumps-Other-Tools-Thinking/d...). I think you are not giving him enough credit. He actually spends most of the book arguing against popular ideas in philosophy that either have no support in science, or have counter-evidence in science. I found the book was written clearly, with very little philosophical jargon.