A new analysis of high-resolution data from the Atacama Large Millimeter/submillimeter Array for five luminous or ultraluminous infrared galaxies gives a slope for the Kennicutt-Schmidt (KS) relation equal to for gas surface densities Σmol > 103 M o pc-2 and an assumed constant CO-to-H2 conversion factor. The velocity dispersion of the CO line, σ v, scales approximately as the inverse square root of Σmol, making the empirical gas scale height determined from nearly constant, 150-190 pc, over 1.5 orders of magnitude in Σmol. This constancy of H implies that the average midplane density, which is presumably dominated by CO-emitting gas for these extreme star-forming galaxies, scales linearly with the gas surface density, which in turn implies that the gas dynamical rate (the inverse of the freefall time) varies with , thereby explaining most of the super-linear slope in the KS relation. Consistent with these relations, we also find that the mean efficiency of star formation per freefall time is roughly constant, 5%-7%, and the gas depletion time decreases at high Σmol, reaching only ∼16 Myr at Σmol ∼ 104 M o pc-2. The variation of σ v with Σmol and the constancy of H are in tension with some feedback-driven models, which predict σ v to be more constant and H to be more variable. However, these results are consistent with simulations in which large-scale gravity drives turbulence through a feedback process that maintains an approximately constant Toomre Q instability parameter.