In simulations involving large deformations, conventional Lagrangian finite element methods often suffer from severe mesh distortion and entanglement, particularly when modeling localized failure in quasibrittle materials. To address these limitations, this work presents an implicit semi-Lagrangian framework based on the Reproducing Kernel Particle Method (RKPM) formulated within a micropolar continuum, providing inherent regularization of shear-dominated failure. The main focus of the study is a comparative evaluation of stabilization strategies for nodal integration within the RKPM framework. Four approaches are investigated: (i) Stabilized Nodal Integration (SNI) employing a novel quasi-conforming update of smoothing domains based on the full deformation gradient, (ii) Naturally Stabilized Nodal Integration (NSNI) derived from a Taylor expansion of the internal virtual work of linear and angular momentum, (iii) Sub-Domain Integration (SDI), which enhances stability through subdivision of smoothing domains, and (iv) Variationally Consistent Integration (VCI) based on a Petrov-Galerkin correction to enforce variational consistency. The performance of these methods is demonstrated through benchmark problems, including a plane strain compression test governed by a Drucker-Prager-based micropolar plasticity model. Comparisons with Finite Element Method (FEM) and Material Point Method (MPM) simulations show that the proposed RKPM formulations robustly capture large deformations and complex failure mechanisms. The results highlight the relative accuracy, stability, and computational efficiency of the different stabilization strategies and their suitability for large-deformation failure analyses.