If it's the first time you've screwed up the return, you might try calling them and ask to have the penalty waived or reduced. That works pretty often on first-time penalties.
I believe your best chance is dialing in right when they open, before the call queues build up. Also the folks answering the calls are in a better mood then, and you're more likely to get the outcome you're looking for.
General penalty relief: https://www.irs.gov/payments/penalty-relief
I just went through this for an honest mistake as well, though I didn't qualify for a first time abatement. It took months to get a response as well.