By "the HWZ sum rule", I mean the Dharwadker-Khachatryan formula that predicted the Higgs mass. (Perhaps we should call it the Dharwadker-Khachatryan sum rule.)
By a "Sumino mechanism", I mean something like Yukinari Sumino's mechanism which allows the Koide relation to be exact within experimental limits, despite the running of the masses.
This thought was prompted by Lykken's talk, mentioned in the previous post, in which a dark matter scalar controls the running of the Higgs mass. Perhaps some version of this model can also protect the DK formula from quantum corrections.