Of the three generational triples, t-b-tau works best (Andrew had to fudge the first generation a little, and the second is completely off); which shouldn't be a surprise, since t-b-c is already known to work well, and the masses of tau and charm are relatively close. It wouldn't surprise me if t-b-tau is already in the Koide-inspired literature (it is, incidentally, common to speak of t-b-tau mass unification in GUTs, but the idea there is that their masses are the same at the GUT scale).
Andrew's paradigm doesn't especially favor consideration of generational triples (with all the non-neutrino fermions of a generation) beyond the first generation. But a more conventional approach might hope to produce such triples through a type of "horizontal symmetry" (that skips the electrically neutral neutrinos). Indeed, one could reasonably also dub a generational triple a "horizontal triple", and a family triple could be a "vertical triple".