Presumably the M_tot includes all the contributions from pressure/energy. I'm not sure about interior solutions, but this is at least the case for the exterior Schwarzschild solution.

The general form of the interior metric of a neutron star is not currently known, as far as I know, because the equation of state of the neutron degenerate matter, rho(P), is not known.

If you did know (or assume you knew) the equation of state, for a static star solving Einstein's equations (the interior Schwarzschild solution) arising from that equation of state would give you the interior metric, and hence the time dilation. If you wanted to go beyond the static approximation (i.e. to include the effects of radiation on the stellar structure), you'd need an even more sophisticated model.