Quote by johne1618
If most of the mass/energy of a proton is due to the kinetic energy of its quarks and gluons, rather than interaction with the Higgs field, then how can we explain its inertial mass, i.e. its resistance to acceleration, as being due to a drag induced by the Higgs field?

You can't. The proton mass has little to do with the Higgs. Therefore its resistance to acceleration has little to do with the Higgs. No one has claimed so.
Quote by johne1618
But the Higgs field is Lorentz invariant so that if the inertial resistance force is due to the Higgs field then it shouldn't be any harder to accelerate the body whether it is spinning or not.

A Lorentz transformation never turns a nonrotating body into a rotating body (though it can affect the linear velocity). So Lorentz invariance doesn't give you any connection between the two configurations.