I have two ideas regarding the "~1/alpha, ~14, ~1/alpha" distribution of mass scales in the plot.
First, let me establish some nomenclature. We have a "light" mass scale for the electron and first-generation quarks, a "pion" mass scale for the muon and the strange quark, a "nucleon" mass scale for the charm and bottom quarks, and a "heavy" mass scale for the top quark. (And a superheavy mass scale relevant for neutrino masses if seesaw mechanism applies; it's not on the plot, but it's relevant if we're trying to explain all the masses.) I'll also note as before that a nucleon has three partons, a pion has two partons, and I speculated that the light mass scale corresponds to a "bare" supercomposite (mesino, diquarkino) in which there are no "dressed" partons.
On the plot we see that the step from light mass scale to pion mass scale is a factor of 1/alpha, the step from pion mass scale to nucleon mass scale is a factor of about 14, and the step from nucleon mass scale to heavy mass scale is another factor of 1/alpha. If you note that 14 is close to 1/sqrt(alpha) (certainly much better than order-of-magnitude close), then it's as if the mass scale goes up by one factor of 1/sqrt(alpha) for each extra "dressed parton".
That would imply that the top quark scale is a "five-parton" energy scale, like a pentaquark that binds a meson-like substructure with a baryon-like substructure. Perhaps the W and Z could also be regarded as heavy four-parton objects. This is all reminiscent of the Calmet-inspired preon model I posted earlier, though that model provides no explanation of why each extra charged parton should contribute multiplicatively, rather than additively, to the mass of a bound state.
The other idea is inspired by Jay Yablon, who you say (in the paper) pointed out the 1/alpha size of the step from tauon mass to Fermi scale. One of Yablon's papers
tries to explain why we see no magnetic monopoles in a fashion inspired by electroweak theory. He posits an SU(2) symmetry between electric charge and "magnetic charge", and a heavy new boson, the "dualon", which has something to do with monopoles obtaining mass. The broader idea is to gauge electric-magnetic duality - the dualon is to be the gauge boson of this symmetry. There is a recent paper
saying you can't do this (in any way known to the authors). Still, even Lubos thought Yablon's paper was intriguing, and somehow similar to one of his own
, on "a general upper bound on the strength of gravity relative to gauge forces".
So this other way to interpret the heavy mass scale where the top quark lives, is as the dualon scale, or perhaps as the dualino scale, and to say that the symmetry between the "zero parton scale" and the "five parton scale" has something to do with electric-magnetic duality. One of our repeatedly examined options here is to explain everything in terms of SQCD, and SQCD provided the original examples of Seiberg duality (a form of electric-magnetic duality), and the relation in the sbootstrap between electromagnetic U(1) charge and SU(3) color charge is certainly not nailed down... So it is not beyond imagining that some version of this is at work.