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 1.74_-0.07_^+0.09^ for gas surface densities {Sigma}_mol_>10^3^M_{sun}_/pc^2^ and an assumed constant CO-to-H2 conversion factor. The velocity dispersion of the CO line, {sigma}_v_, scales approximately as the inverse square root of {Sigma}_mol_, making the empirical gas scale height determined from H~0.5{sigma}^2^/({pi}G{Sigma}_mol_) nearly constant, 150-190pc, over 1.5 orders of magnitude in {Sigma}_mol_. 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 {Sigma}_mol_^1/2^, 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 {Sigma}_mol_, reaching only ~16Myr at {Sigma}_mol_~10^4^M_{sun}_/pc^2^. The variation of {sigma}_v_ with {Sigma}_mol_ and the constancy of H are in tension with some feedback-driven models, which predict {sigma}_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.