One option you have is to recharacterize your Roth IRA contribution as a Traditional IRA contribution. Basically this means pretend as if you originally made a Traditional IRA contribution instead of a Roth IRA contribution. There are no income limits for contributing to a Traditional IRA, so it won't be an excess contribution. (There are income limits for deducting a Traditional IRA contribution if your or your spouse is covered by a retirement plan at work, but you are not going to deduct it.)
Then, you would convert all the money in the Traditional IRA to a Roth IRA. There is no income limit for conversions either. (You are basically belatedly doing a "backdoor Roth IRA contribution".) Assuming you had no pre-tax money in IRAs (and won't put any pre-tax money into IRAs this year), during the conversion, the after-tax contribution portion of the Traditional IRA won't be taxed; only the earnings part since you contributed until the conversion (which is probably a very small amount) will be taxed. So the end result is basically the same as what you have now, with no penalties.