> Note that the Higgs Boson has no part in the mass (and presumably gravitational interaction) of elementary fermions like quarks or electrons

This is incorrect — the coupling with the Higgs field is responsible for the rest mass of electrons and isolated quarks.

> and even less to do with the mass of hadrons

Yes, this is true — the contribution of the separate masses of the constituent quarks to the mass of hadrons is small, like you write.