Post another tough one if you would like an analysis like the others. I don't want to spoil the fun for you or the others, but it might save you stacks of paper (and time) like I used.
If you see a few of these intial stage walk-throughs, you will start to see the combinations that get you through the crux of the puzzle.
When I finally started to solve the tougher ones, I immediately solved the same puzzle from scratch to make sure I didn't get stuck by the same hidden clue. I.e. I wanted to make sure I actually learned something that I could use in the next puzzle.