In previous work, three implicit potential energy surfaces with specific reaction parameters (SRP), namely MPW60, MC-QCISD-SRP, and MCG3-SRP, were developed for the reaction CH4+H-->CH3+H-2. Forward reaction rate constants obtained by variational transition state theory with multidimensional tunneling (VTST/MT) dynamics calculations on these surfaces give good agreement with recently re-analyzed experimental results. In the present work, again employing VTST/MT, kinetic isotope effects (KIEs) for isotopic variants of the title reaction in both the forward and reverse directions are examined on these SRP surfaces. Various primary and secondary deuterium (D) kinetic isotope reactions are studied; we also calculated the KIE for the reaction between methane and muonium (Mu), which is an ultralight isotope of protium with the Mu/H mass ratio being 0.113. The results are compared with several sets of experimental studies. With the VTST/MT dynamical method and harmonic vibrations, the proposed surfaces predict the KIE quite well, probably within experimental error, for seven different isotopic combinations involving substitution of one to five deuteriums for protium. The calculations also reproduce quite well the high Arrhenius activation energy for Mu+CH4, and the KIE for muonium atom attack is correctly predicted to be inverse, but the predicted values of the Mu KIE over the experimental temperature range are 0.012-0.06 (without scaling force constants) or 0.021-0.09 (when the force constant of the making bond is scaled), whereas the experimental values in the same temperature range are 0.05-0.3. Several possible reasons for this are discussed.