In that car, run premium. That engine is designed around the supercharger. Even when it's not providing positive pressure, it's still providing more pressure than what the atmosphere can force in by itself.
The L67 was never meant to run on regular. It's designed and tuned for running premium, with some skimpy backup low-octane tables in the PCM just in case there's a natural disaster and the sole gas station left open is only pumping regular.
Premium will provide better fuel economy, more than making up for the extra $4-5 a tank when going another 50-60 miles a tank.