Accurate quantum mechanical scattering calculations for the reaction of D with H2 are analyzed for evidence that quantized transition states control the reaction dynamics over a wide range of total angular momenta. We find that quantized transition states control the chemical reactivity up to high energy and for values of the total angular momentum (J) up to at least nine. We show that the average transmission coefficient for individual dynamical bottlenecks up to 1.6 eV is greater than 90% for all four of the values of J considered (J = 0,3-6,9). We assign energies, widths, level-specific transmission coefficients, and quantum numbers to eleven transition state levels for J = 0 and two for J = 1, and we show how a separable rotation approximation (SRA) based on these data predicts thermal rate constants for temperatures between 500 and 1500 K that are within 0.3%-5.0% of the values obtained from accurate quantal scattering calculations up to high J. This implementation of the SRA enables us to quantify the contribution of each transition state level to the thermal rate constant, and to separately quantify the influence of recrossing and of quantum mechanical tunneling and nonclassical reflection on the thermal rate constant. Finally, we demonstrate the influence of two supernumerary transition states on both the overall and the state-selected dynamics.