I think I'll weigh in on this, since I've been reading the disagreement going on over Duty specifically.
In Japanese (not Rokugani) history, Duty was owed in a 3-fold manner. Duty to your Family/Friends being least important, Duty to your Lord being the middle, and Duty to the Emperor/Shogun being highest.
Hence, in the classic 47 Ronin story, the Ronin do their Duty to their Daimyo in avenging him, then commit seppuku because their Duty to Imperial Law demands it for breaking the decree against violence.
If we translate that to L5R, then first of all, we are possibly getting way too minute in detail by disassembling individual Virtues. But, on the offhand chance that anyone is interested in working such the proposed scenario from a few pages back might go in the following way:
Daimyo says go murder peasants to deny them to the enemy. Samurai has a choice to make, depending on whether s/he holds Bushido or their Daimyo in higher esteem (while the obvious answer is Bushido for Rokugan, consider how a loyal vassal might consider their lord to be wiser in its ways than they, and infer that any order that they give will be in keeping with the most Honorable path according to Bushido. Trust can be a terrible thing.). Either way, the choice they make, be it blind acceptance, refusal, or protest kanshi, will be the "honorable" choice, as it is the thing they hold to be most in keeping with the tenants of Bushido.
Society might say differently, of course, but it is easy enough to say that the Samurai caste (certain poorly thought out schools aside) are conditioned to take what they perceive as the most honorable option at all times. Even the Scorpion are working under this assumption, because their core tenant of Loyalty refers not only to the Clan, but the Empire as a whole. Even Assassination can be an honorable act, so long as it is done for the good of the Empire, or so the Scorpion mindset works.
So, I suppose a modification that I might offer to the original thought of your Honor being based on your 3 lowest virtues would be that it be calculated off your 2 lowest + the Virtue held dearest by your Clan. Clan is one of the defining aspects of any Great Clan character after all. This is obviously not a perfect solution, as the Mantis and Spider kinda get blindsided here (Maybe run off of Shourido "virtues"?) and it doesn't do much for Non-Great Clanners, but then again, the grand majority of Non-Great Clan Samurai really don't have to worry about Honor, because the society that it is based around is entirely ambivalent to their existence. Being a non-samurai in Rokugan just sucks (Less so in Unicorn lands, but it still sucks pretty hard. Simple life of back-breaking labor vs. Simple life of back breaking labor plus possibly getting murdered for little to no reason by your lords.)