Unrestricted single-point matching is too weak

The construction solves a chosen algebraic equation. It does not extract $h$ from independent operational geometry. Likewise, defining ${\tau }_D={{\kappa }_{\mathrm{cmp}}}^{-1}{\mathsf{E}}_{\eta }(j_D)$ would make the residual vanish by definition, but would not prove that this tensor is independently identified matter stress-energy.

A prescribed Einstein inverse can provide a valid conditional classical response construction. It does not, by itself, derive Einstein dynamics from process data.