The asymptotic Narimanov-Moiseev–type discrete dynamical system which effectively classifies resonant sloshing in a square base tank when the forcing frequency is close to the lowest natural sloshing frequency is employed to show that orbital elliptic translational excitations can, depending on the semi-axis ratio of the elliptic orbit, lead to both the counter- and co-directed (relative to the orbital forcing direction) stable swirling-type steady-state resonant waves. For non-zero damping in the hydrodynamic system, circular excitation makes the stable counter-directed swirling impossible. Stable and unstable solutions, their bifurcations are specified on amplitude response curves to identify multi-stability and chaos.