Bumping the thread to update - I contacted LH via email twice, and both occasions got responses from agents who either suggested itineraries that won't fare, or flying from LON via TYO. Despite some very patient and clear explanation from me, nobody has yet understood that I think there's a *problem* they should look into.
I might try contacting LH's UK office. If the missing fares really are affecting a number of UK airports, surely they would have noticed by now?