It would be exciting if I “guessed wrong”, and I think I did. If the mass, previously considered as a black hole, were spread out to a larger radius r_0, then the integration for total proper distance only starts at this point. I email my oh brother::
I will try to complete this little study, expanding a BH’s mass to some point…even if part of this integration “excess” remains, isn’t it news?
If this holds up, then the formation of black holes as the Universe ages does change things, blows it out some. Either way, it is a far-field effect of the Schwarzschild.