I have the issue where if I'm stuck on a problem and try to sleep on it, I wake up as tired as if I had stayed up working. My brain seems to never completely shutdown and rest. Have you ever experienced that? Any suggestions?

I guess I don't try to "sleep on it". I just tell myself I'll tackle it another time and go to bed. I have amazing sleep hygiene and I tend to use one dream from a set of dreams to fall asleep. Somehow I still wake up and have the solution the next day even though it was never my intent.