Spherical CR uniformizations of a sequence of hyperbolic 3-manifolds

Let $s782$ be the 2-cusped hyperbolic 3-manifold in the SnapPy census. Its spherical CR uniformization was established in \cite{JWX2023} using the Ford domain of the complex hyperbolic triangle group ${\mathrm{\Delta }}_{4,4,\mathrm{\infty };\mathrm{\infty }}$. By comparing the combinatorial structures of the Ford domain of ${\mathrm{\Delta }}_{4,4,\mathrm{\infty };\mathrm{\infty }}$ and the Dirichlet domain of ${\mathrm{\Delta }}_{4,4,n;\mathrm{\infty }}$, we prove that for each $n\ge 5$, the Dehn filling of $s782$ along the slope $(n-1){\mathcal{m}}_1+{\mathcal{l}}_1$ on its second cusp admits a spherical CR uniformization, where $({\mathcal{m}}_1,{\mathcal{l}}_1)$ denotes the meridian-longitude system of a cusp in SnapPy notation.