I actually want to disagree with Todd here.
I definitely agree that the first point of contact should be email@example.com. We're friendly and helpful and want to resolve problems that generated suspensions or deletions, privately and constructively. (Of course, I would say that, wouldn't I? In any case, it's the truth.)
But what should happen when you can't resolve your difficulties with the moderators?
The best answer is probably that you should make the best of the situation, and leave MathOverflow for other online mathematical communities. But what if you want to appeal?
Todd says that you should take your case to the Stack Exchange Community Moderation team. I disagree. Writing to firstname.lastname@example.org is not a bad idea --- they are sensible and helpful people too, and in all probability they'll do a good job of helping you understand whatever it is that you're having trouble understanding while communicating with the moderators. But don't think of it as an appeals process --- they're not going to get involved in that sense.
Instead, following the long tradition of MathOverflow, you could bring the case here, to meta (ah, how I miss tea). Such an appeal would require stating the case clearly, and at the same time waiving one's right to the privacy of their previous email communications with the moderators. We would then respond, in this case at considerable length. The MathOverflow community matters. We will listen if there is widespread community consensus, even if it directly contradicts the position we've taken previously. In an egregious enough case, moderators would resign if the community decided they'd been behaving inappropriately.
In this particular case, I would strongly not recommend considering this approach. I predict that it would go very badly. We far prefer to deal with these problems privately, but if we really needed to do it in public we could. It would not be pretty.