As $|s|\to\infty$ one can choose smooth portions of the hypersurfaces $Z_{s}^{\mathrm{sm}}\subset Z_{s}$, the embeddings $\psi_{s}:Z_{s}^{\mathrm{sm}}\hookrightarrow W_{s}$ and a family of Kähler metrics on $Z_{s}$ in the class $\frac{\nu_{0}}{\log|s|}(1+o(1))$ such that the pairs $(Z_{s},Z_{s}\backslash Z_{s}^{\mathrm{sm}})$ converges to the pair $(\Sigma,D)$ in the Gromov-Hausdorff sense, and the maps $\psi_{s}$ identify (uniformly in $x\in Z_{s}^{\mathrm{sm}}$) the scalar products and the complex structures on the tangent spaces $T_{x}Z_{s}$ and $T_{\psi_{s}(x)}W_{s}$ up to terms of order $o(1)$.