The swap Monte Carlo algorithm allows the preparation of highly stable glassy configurations for a number of glass-formers, but is inefficient for some models, such as the much studied binary Kob-Andersen (KA) mixture. We have recently developed generalisations to the KA model where swap can be very effective. Here, we show that these models can in turn be used to considerably enhance the stability of glassy configurations in the original KA model at no computational cost. We develop several numerical strategies both in and out of equilibrium to achieve this goal and show how to optimise them. We provide several indicators, together with mechanical and thermodynamic signatures of enhanced stability, including a clear transition towards brittle yielding behaviour.