That's false. Uniform gravitational potentials are can create acceleration if the potential changes. In a uniform Newtonian universe the gravitational potential will change with density, you can get acceleration in time even though the potential in space is constant.Thus there is no difference between the gravitational potentials at A and B and thus there should not be any relative acceleration between them.
I wouldn't even bother trying to derive anything at this point. Assume R=ct, and the figure out the observational consequences. If we actually observe the universe fitting R=ct then we can let the theoreticians loose. If R=ct, theoreticians can come up with a hundred reasons why R must equal ct. If R doesn't equal ct, theoreticians can come up with a hundred reasons why R can't equal ct.(I personally think his R = ct Universe is still valid but that it has to be derived by assuming that the gravitational potential has the value [itex]-c^2[/itex] at every point. Thus every particle's rest mass energy [itex]m c^2[/itex] is balanced by its gravitational potential energy [itex]-m c^2[/itex] giving a zero-energy Universe. The radius of the spherical mass around each point required to produce this potential is what Melia calls the gravitational radius.)