I was immediately drawn to your illustration, and I can see that it is a good representation of not just the problem solving technique, but the problem itself. I took a couple problem solving classes and loved every part of them, because a) I love to analyze and b) I love to get to the truth. I think to solve hard problems you need to start with 'what is' and peel back the layers until you get to the root cause, clear the board and put back the pieces that need to be there.  It takes a long time, but I think it takes less time and you get much better results and have what 'should be'.  Do-overs and re-work because you settled are not going to take more time and cost more in the end.