  In recent years, the techniques of analytic combinatorics in several
variables (ACSV) have been applied to determine asymptotics for several
families of lattice path models restricted to the orthant $\mathbb{N}^d$ and
defined by step sets $\mathcal{S}\subset\{-1,0,1\}^d\setminus\{\mathbf{0}\}$.
Using the theory of ACSV for smooth singular sets, Melczer and Mishna
determined asymptotics for the number of walks in any model whose set of steps
$\mathcal{S}$ is "highly symmetric" (symmetric over every axis). Building on
this work, Melczer and Wilson determined asymptotics for all models where
$\mathcal{S}$ is "mostly symmetric" (symmetric over all but one axis) *except*
for models whose set of steps have a vector sum of zero but are not highly
symmetric. In this paper we complete the asymptotic classification of the
mostly symmetric case by analyzing a family of saddle-point-like integrals
whose amplitudes are singular near their saddle points.
