I would stick close to the original estimate and consider it a learning experience. Being able to estimate fairly accurately is part of your business and you need to be able to do it accurately. My husband and I have been in business for 30 years. There have been times when we have lost money on a job because we took longer than estimated to complete the job. Its part of being in business.
Also, as a customer, I had a show car painted. I let the guys who were painting it decide what methods they would use. They chose one that took longer and made them run over their estimate. They decided since I was a good customer to eat the extra because they made the decision on method. They have done things like this before and therefore I'm a repeat customer.
It's kind of an individual decision. You have to think about all aspects and whether you want (or may get) repeat business from this customer.