I've had more ideas come to me after hiding in my office to take a nap than sitting at my desk. It got to be such a gold mine of solutions that I still to this day allocate 30 minutes of my day to a nap. Non-negotiable. So many hard problems that have been brought to me, or complicated needs for architecture, etc were solved by simply turning my active brain off. When I was in graduate school I'd regularly get stuck…
Many of the hard problems in my career have been solved while having a long warm shower in the middle of the work day.
In general, my own productivity trick is understanding and leveraging the Eureka effect. Your subconscious is still working on the problem when your conscious mind is doing something else. Often, if pointed focus doesn't work, just leave it in the back burner to stew. Then wait for the proverbial light bulb to show you the way, out of nowhere. It never fails, yet I have never heard anyone mention this phenomenon.
My empirical explanation is hard problems benefit from unrelated stimuli, so they're able to be approached from an oblique direction. In other words, to think out of the box, stop thinking and do something else.