  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.
