You are certainly at least partly right. But:
After all, "contraband" methods of persuasion are rarely punished
Contraband methods of persuasion are weakly punished, here and elsewhere, by means of public humiliation along with repudiation of the point trying to be made. Some people go so far as to give fallacious defenses of positions they hate (on anonymous forums) in order to weaken support for those positions. Interestingly, the contexts where we think logic is most important (like this site) are much less tolerant of fallacies than the contexts where we think logic is less important (politics or family dinner). So while I'd love to dismiss that cynical explanation, I can't quite so easily.
People often have conflicting intuitions, but there seems to be some hierarchy which tells which intuitions are more basic and thus to be preferred.
Actually, there is indeed such a hierarchy in moral reasoning, and it has been better studied/elucidated (by Kohlberg, Rest, et al) than logical reasoning has.
lukeprog gave a list of metaethics questions here:
Most of these questions make no sense to me. I imagine that the moral intuitions in my brain come from a special black box within it, a "morality core" whose outputs I cannot easily change. (Explaining how my "morality core" ended up a certain way is a task for evo psych, not philosophy.) Or I can be more enlightened and adopt Nesov's idea that the "morality core" doesn't exist as a unified device, only as an umbrella name for all the diverse "reasons for action" that my brain can fire. Either perspective can be implemented as a computer program pretty easily, so I don't feel there's any philosophical mystery left over. All we have is factual questions about how people's "morality cores" vary in time and from person to person, how compelling their voices are, finding patterns in their outputs, etc. Can someone explain what problem metaethics is supposed to solve?