Dehn-surgery conjecture for the manifolds at infinity of $\Delta_{3,4,\infty;n}$

Let $\Delta_{3,4,\infty;n}$ be the complex triangle group with parameters $3,4,\infty;n$, and let its even subgroup be the subgroup considered in the paper. Let $m295$ be the two-cusped hyperbolic $3$-manifold in the Snappy Census. The manifold at infinity is the $3$-manifold associated with the group's spherical CR uniformization.

Dehn-surgery conjecture. The manifold at infinity of the even subgroup of $\Delta_{3,4,\infty;n}$ is the hyperbolic $3$-manifold obtained by Dehn surgery on the first cusp of $m295$ with slope $n-2$.

The case $n=\infty$ is related to the known identification of the manifold at infinity of the even subgroup of $\Delta_{3,4,\infty;\infty}$ with $m295$. The conjecture predicts that varying $n$ produces further spherical CR uniformizations through Dehn surgeries on that cusp; the source gives no resolution of the general claim.