Probably not great advice if you're looking specifically for a practice that'll quickly teach the habit of carrying tactical decisions through into strategic goals -- in this context that's something you only get from lots of blade-to-blade practice, and the koryu arts are almost universally very heavy on kata. In a typical dojo you might not get to freestyle sparring for a year or more. Western reconstructionist fencing tends to be less so, but there's still a pretty serious ramp-up period in every salle I've ever been exposed to.
On the other hand, if you can get past that period, just about any martial art which involves partnered practice is remarkably good at developing the skill of instrumentalizing strategic thinking (though it still needs to be generalized to the rest of life, a difficult trick which probably qualifies as a virtue of rationality in its own right). Weapon arts (and aikido, but it's unique in this respect among the empty-hand arts I've studied) are also good for developing a habit which is difficult to put into words, but which might be approximated as "presence" or "mindfulness".
Recent brainstorming sessions at SIAI (with participants including Anna, Carl, Jasen, Divia, Will, Amy Willey, and Andrew Critch) have started to produce lists of rationality skills that we could potentially try to teach (at Rationality Boot Camp, at Less Wrong meetups, or similar venues). We've also been trying to break those skills down to the 5-second level (step 2) and come up with ideas for exercises that might teach them (step 3) although we haven't actually composed those exercises yet (step 4, where the actual work takes place).
The bulk of this post will mainly go into the comments, which I'll try to keep to the following format: A top-level comment is a major or minor skill to teach; upvote this comment if you think this skill should get priority in teaching. Sub-level comments describe 5-second subskills that go into this skill, and then third-level comments are ideas for exercises which could potentially train that 5-second skill. If anyone actually went to the work of composing a specific exercise people could run through, that would go to the fourth-level of commenting, I guess. For some major practicable arts with a known standard learning format like "Improv" or "Acting", I'll put the exercise at the top and guesses at which skills it might teach below. (And any plain old replies can go at any level.)
I probably won't be able to get to all of what we brainstormed today, so here's a PNG of the Freemind map that I generated during our session.