I can relate to your strategy of writing, solving, failing, forgetting. I've been going through the book Calculus by Spivak, and there have been times where I've pushed through for hours and hours on a problem, only to forget about it for a while and come back with a fresh mind and solve it pretty quickly. I found it funny how you described the failure part. Yes, if a problem is super, super hard and you have been at it for hours you may start to question everything you are doing with your life and your time! But deeply thinking (and this part involves all you wrote about subtlety and looking at a concept from various angles and perspectives through problem solving) does bear fruit. Many times you only realize this whenever and however you get past what you were stuck on and realize that you have all of a sudden become much more comfortable with various other concepts that were foundational to the one you were working on. I would love to know where you are in your self-studies of math and where you're going?