But what if I extended my (imaginary) offer of wireheading to two years, or ten years, or the rest of the person's natural life?

If I don't want wireheading at all, increasing the offered amount of it makes it even worse.

The reason I ask is that most people here, myself included, have a strong aversion to wireheading; but I want to figure out if this aversion is rational, or due to some mental bias.

Well, why do you not want to wirehead? Or for that matter, why do you think it is rational to want to? You haven't atually said, just posed what looks like a rhetorical question, "why would one not?", that simply presumes it to be obviously desirable, requiring some special effort to demonstrate otherwise.

I can see how someone might philosophise themselves into that position, along these lines: pleasure is by definition what we want; therefore wireheading in a machine that delivers maximal pleasure must, if available, be the thing we want most. Is that what you have in mind?