I don't recommend the method used by an Electrician we worked with a couple of years ago. It was a mid-sized commercial job, so that makes it quite a bit different from your situation, but this guy's change orders were literally 10 grand for an additional receptacle. I'm pretty sure he waaaay under-bid in order to get the job and was trying to make up his losses on the change orders, but he took it too far and made it too obvious.
Needless to say, the customer said, "Never mind; I don't need that extra receptacle that badly," and then hired somebody else to put it in after getting the final. Oh, and they blacklisted the original EC; won't ever work with him again.
That being said, you still deserve just compensation for your extra work. Human beings are notorious for getting a number fixed in our head and not wanting to deviate from that number, so I could easily see the homeowner saying, "But you quoted me $XXX for the job, why are you trying to jack up the price now?" That's when you need to gently remind him that the original price was for the original scope of work, and that more labor and materials equals an increase in price. The "gently" part is, I believe, an art form in and of itself, and those who are good at it tend to get more repeat customers.
The good thing about using a simple formula like "Material + Labor + Profit = Price" is that you can show it to your customer so he will understand why? it costs what it does. If he's a reasonable person, he should accept it and move on.