Gravitational mass and inertial mass are equivalent under the weak argument of General Relativity. Graitons are supposed to mediate the force of gravity on long distances, whilst inertial mass itself is strictly provided by a Higgs Boson.
Would it not be better to say a Higgs provided inertia rather than a graviton, who's job is to send quatum force signals over distances?
There are two old papers by Weinberg in which he demonstrates that the quantum theory of a massless spin-2 particle gives you GR so long as you impose the condition that the S-matrix is Lorentz invariant, plus one other condition in each paper. I can't follow all of the arguments, but in case you can:
Weinberg, S;Phys Rev. vol 135, 1964;
-Makes additional assumptions about the pole structure of the S-matrix to demonstrate the equivalence of gravitational and inertial mass.
Weinberg, S;Phys. Lett. vol 9, 1965
-Uses perturbation theory to derive Einstein's equations under the additional assumption that effectively helicity =[tex]\pm[/tex]spin for massless particles.
To boot, he also treats electromagnetism in each, showing the conservation of charge and deriving Maxwell's equations under the same assumptions, but assuming instead the existence of a massless spin-1 particle.