We introduce a polydisperse variant of the binary Kob-Andersen Lennard-Jones mixture designed to study glassforming liquids in the deeply supercooled regime far below the mode coupling temperature TMCT. Incorporating polydispersity enables efficient swap Monte Carlo moves, facilitating equilibration in this otherwise inaccessible regime. Under shear, the yielding of the system is associated by a solid-like response at low shear rates, manifested by sharp stress drops and shear banding. By abruptly varying the shear rate, we investigate pronounced memory effects. In particular, switching to a lower shear rate induces a stress minimum, a universal feature of glassformers recently observed in metallic, colloidal and polymeric systems. Using different shear-rate switching protocols, we demonstrate the occurrence of the Kovac effect in deeply supercooled liquids under shear.