Thanks to spotty internet and power outages, there was time to do some serious off-and-on samuraiing these past couple days, and I got my unsurpassed honor.
Theory: we can't get this level if we either 1) play all the way through with our original samurai, rather than a successor, or 2) assassinate either our Hatamoto or Diamyo lords. It could be either one, since those are the two main differences between this game and my previous attempt.
The highest honor my samurai could get in any case was "extreme" until he was made the Daimyo of the clan. Once he succeeded the old Daimyo, he immediately passed the rank on to his son, the third generation Youth. This kid pulled off this honor stunt within a few turns by winning a typical "wandering duelist who defeats all comers" encounter. According to the hex data in the save game, Honor rose from 7A (122) to 80 (128) in this encounter. So that's how that goes, just for anyone who gets stumped.