How does one then answer the question “If you think elections don’t work, then why do you participate?” by a non-anarchist?

You've made plenty of good points throughout the article about the problems with the system. I don't see why that can't be your answer. There's no contradiction in acknowledging major problems and still exerting what little influence you do have.

But if they “work a little” for an anarchist, certainly they would work a lot for a non-anarchist.

How does that logic follow? Assuming you both have the same values and are trying to achieve the same thing, then a solution that works for one person will work just as well for another. The difference in opinions is on which solution will work, not on what you're trying to achieve.