The interplay of interactions between aqueous ions and the confinement of subnanoscale pores in solid 2D membranes causes a range of barrier-limited phenomena, including selective ion trapping and permeation, mechanosensitive transport, and memristive effects. A clear understanding of the transition from diffusive to barrier-limited transport regime is lacking, however. Moreover, the limits of applicability for the analytical formalism widely used to relate measured transport data to the effective pore size are unclear. Here, with the goal of identifying the transition between regimes and determining the pore sizes below which the diffusive formalism fails, we present a computational study of water-dissociated alkali salt transport through 2D membranes featuring pores of various sizes. Triangular nitrogen-terminated multivacancies in hexagonal boron nitride are used as a simple yet illustrative example of uncharged locally dipolar pores with various degrees of cation selectivity. We find that