Up to slightly shrinking the domains, the Calabi-Yau metrics on $U_{J,t}$ admit local potential functions $\phi_{CY,J,t}$ such that $\omega_{CY,t}=dd^{c}\phi_{CY,J,t}$, and $\left\lVert\phi_{CY,J,t}-\phi_{0}\circ\text{Log}_{\mathcal{X}}\right\rVert_{C^{0}}\to 0$ as $t\to 0$.