After briefly reviewing the potential for the $N$-flavor Thirring
model, formulated with reducible fermions in 2+1$d$, to exhibit a
strongly-coupled UV-stable fixed point where U($2N$) symmetry is spontaneously broken
by a fermion bilinear condensate, we present recent lattice studies
using the Domain Wall Fermion formulation. In particular, we focus on possible
improved methods for extracting the necessary $L_s\to\infty$ limit, where $L_s$ is the wall
separation, through a combination of partial
quenching (ie. $L_s({\rm valence})>L_s({\rm sea})$), replacing the Shamir kernel
with the Wilson kernel in the definition of the overlap operator, and improved
estimation of the signum function using the Zolotarev approximation. Equation of
state fits for critical exponents
on $12^3$ systems yield encouraging agreement between
distinct approaches, consistent with universal scaling, while contradicting earlier fits based on a naive
extrapolation. The new results are also in tension with old results obtained with
staggered fermions.