Variational transition state theory (VTST) with an adiabatic approximation for excited vibrational modes and semiclassical transmission coefficients to account for tunneling is used to calculate state-specific reaction rates for the collinear reaction H+F2(n=1)→HF+H and the three-dimensional reaction Cl+H2(n=1-4,7)→HCl+H, where n is the initial vibrational quantum number and the rate constants are summed over final vibrational states. We also consider deuterated and tritiated analogs for both reactions for n=1. The results are compared to previous state-selected rate constants calculated without transition state assumptions. Comparisons to accurate quantal results for the H+F2 series test both the semiclassical tunneling methods and the validity of the adiabatic approximation for excited-state dynamical-bottleneck locations. Comparison to quasiclassical trajectory calculations for the Cl+H2 series provide further tests of the adiabatic approximation. In general the VTST/adiabatic-plus-tunneling calculations are quite successful.