Use of the reaction-path Hamiltonian in natural collision coordinates with WKB eigenvalues for stretching vibrations is tested for predicting state-specific vibrationally adiabatic barriers for the fully three-dimensional reaction F + D2→FD (n′ = 4) + D. A range of potential energy surfaces, including one specifically designed to have no delayed threshold for the highest energetically allowed product vibrational state, are considered, and both approximate quantal scattering calculations and quasiclassical trajectory calculations are performed for comparison to the adiabatic predictions. We find that the adiabatic predictions correlate well with the quantal scattering results. We also study other features of the dynamics on the surface with no delayed vibrational threshold to see how changing the surface to eliminate the delayed threshold affects other reaction attributes. We find that the approximate quantal differential cross sections for this surface show an appreciable probability for forward scattering of the products. This trend is not exhibited by the quasiclassical trajectory calculations for the same surface.