The inclusion of nuclear quantum effects (NQEs) in molecular dynamics simulations is one of the major obstacles for an accurate modeling of molecular scattering processes involving more than a couple of atoms. An efficient method to incorporate these effects is ring polymer molecular dynamics (RPMD). Here, we extend the scope of our recently developed method based on non-equilibrium RPMD (NE-RPMD) from triatomic chemical reactions to reactions involving more atoms. We test the robustness and accuracy of the method by computing the integral cross sections for the H/F + CH4/CHD3 reactions where the methane molecule is either initially in its vibrational ground or excited state (C-H stretch). Furthermore, we analyze the extent to which NQEs are described by NE-RPMD. The method shows significant improvement over the quasiclassical trajectory approach while remaining computationally efficient.