There are other problems, like how one constructs gravitational-strength interactions for gravivectors and graviscalars.
One can see where the problem will be by doing dimensional analysis of possible interactions. One sets hbar = c = 1 and finds what powers of mass the coupling constants are. Mass = 1/length in these units. I'll be doing the calculations for 4D space-time, but they can be extended to additional dimensions.
The field is given by D2(field) = (coupling constant) * (source density)
and the resulting potential energy is (field) * (source density) integrated over 3-volume.
If the source current has dimension L-s or Ms, then the coupling constant has dimension M6-s.
For electromagnetism and similar theories, the current has dimension L-3, since its integral over volume is a dimensionless number in hbar = c =1 units. That means that the electric charge and other gauge "charges" are dimensionless.
For gravity, the current is the energy-momentum tensor, an energy/momentum density/flux. Its dimension is M*L-3 = M4. The coupling constant has dimension M-2, in agreement with
(gravitational constant) = 1/(Planck mass)2
So one has to construct currents with dimension M4 for the gravivector and the gravivector.
For the graviscalar, there's a current that's very easy and gravity-related. Contract the energy-momentum tensor over its indices, giving
(mass/energy density) - 3*pressure.
For the gravivector, it's much more difficult. I've done a lot of searching, and I can't find what would be a sensible sort of source current.
One can construct (some mass) * (gauge-theory vector current)
where (gauge-theory vector current) is what one gets out of electromagnetism, for instance. For an elementary-fermion field, that current is
j^\mu = {\bar\psi} \gamma^\mu \psi
What would be an appropriate mass here?
But this sort of term has the property that matter-antimatter interchange will reverse its sign, unlike the case for gravity and my graviscalar interaction. It will also yield the "mass"
M_{gravivector} = \sum_{flavor\ i} m_{(i)} N_i
where Ni is the number of elementary fermions with flavor i (ordinary particles - antiparticles), and m(i) is the mass value associated with flavor i.
For an atom with Z protons and N neutrons, this gives us
Mgravivector = m(electron)*Z + m(up quark)(2Z+N) + m(down quark)(Z+2N)
Photons and gluons don't enter, because they are their own antiparticles.
The overall mass is approximately mnucleon(Z+N)
The average N/Z is 0 for hydrogen-1, 1 for the lighter elements, and greater than 1 for the heavier elements, going up to 1.5 near uranium.
So the ratio of these masses is about the ratio of m(flavor) for electrons, up quarks, and down quarks to mnucleon.