A body of salt-stratified fluid in a vertical slot can undergo double-diffusive instabilities when laterally heated. A previous study has indicated the possibility that vibrations could induce instabilities in the cases of a strong salinity gradient in regimes that are not only linearly stable, but also nonlinearly stable. We investigate this limit using the method of averaging and confirm that any level of high-frequency vibrations will lead to a reduction in the heating required for instability for a sufficiently strong salinity gradient, but that this is probably not of great importance to terrestrial experimenters.