You take the extra money and redistribute it. Either as a refund on your registration based on miles driven (meaning more efficient cars get more back than they spent) or as a straight up income tax credit for the poor.
If the excuse to raise the gas tax is to reduce driving, then using the money collected to reduce the pain of the gas tax is in direct conflict with the excuse in the first place and it turns into straight redistribution of wealth. Nice bit of smoke and mirrors.
If you did it as an income tax credit it would reduce driving because a lot of the poor people who would get money don't drive, and more importantly, people are much more psychologically motivated by a $100 fill-up than a year-end tax credit.
