Have you tried this? And if so how did you find it?
Shower thoughts and driving and being unable to sleep at night, like many people, and noticing that my thoughts during those <2 hour periods were 10x as valuable as all the thinking during the rest of the day.
But then, instead of using showering or driving or nighttime to think, I tried staring at the wall with a pen and paper for four hours, and no screens or books, and my thinking was another ~10x as valuable that way.
I was inspired by your post to actually attempt this.
I sat on a chair in an empty office facing a wall with a water bottle, pen and some blank palm cards. I was interrupted when the lights in the office went out automatically one and a half hours in and during the walk downstairs to turn them back on I decided to end the experiment. I openly admit this was a failure of will.
Previously I've done Sam Harris style meditation on and off, usually in periods around 10 minutes. The longest I've ever meditated for in a single session is 40 minutes.
Overall observations:
Some low-level attention holder is good, may be music, driving or eating(!)
Meditation while staring at a mandala for hours is possible. No I can't do it.
Walking a very long distance (15km+), preferably in a not too exciting place (eg residential streets, fields), while thinking, maybe occasionally listening to music to reset. Works best in daylight but when it’s not too bright and sunny and not too warm / cold.
You seem to restrict "rationality technique" here to "methods for thinking hard".
But there are others things one can do. If the topic you are interested in might have a lot of prior research, it can be useful to find and read that research, since you are unlikely to singlehandedly outcompete the work of dozens of other researchers who came before. Better stand on the shoulders of giants than to climb on a stool you made yourself. Or, rather, it's of course the best when you do both to some degree. I'm not sure what the proportion should be.
The problem with reading lots of research is similar to thinking hard. It is difficult to motivate yourself to do it. In particular, research papers can be very difficult and boring. But they become much easier after you read a few. Those people are also just cooking with water.
In general, everyone knows how to use Google to find info. But for research I particularly recommend search engines for papers. Namely scholar.google.com and semanticscholar.org. Each has some papers the other hasn't, so both might be worth a try, although I mainly use the first. In any case, those websites let you explore "related" or "similar" papers, or papers who cite a particular paper. The weakness of those search engines is that they mostly only cite single journal entries or similar, but book chapters are largely missing.
Of course I might be off track here. Perhaps you want to think about stuff that isn't covered by research. For example, about what to do / choose in some difficult decision situation. Here, other things might help, besides thinking hard. Writing down pros and cons for example.
I'm wondering if one exists, and what is the name of that technique or that family of techniques. It seems like something that CFAR has researched extensively and layered a lot of things on top of.
4 hours is necessary for anything substantially longer than 1-2 hours, since 6 hours is too long under most circumstances. Obviously, whiteboards and notepads are allowed, but screens and books absolutely must be kept in a different room. I'm not sure how sporadic google searching and book-searching and person-consulting factors into this, because those queries will suck you in and interrupt the state.
If people are using sleep deprivation, showers, lying in bed, or long drives to think, it's probably primarily the absence of interruption (from books and screens and people) that triggers valuable thoughts and thinking, not the tasks themselves. (although freeway driving might potentially do more good than harm by consistently keeping certain parts of the brain stimulated).