In the case you describe, the “HSC content” is just that Jesus is magic. So there’s no argument being offered at all. Now, if they offer an actual argument, from some other p to the conclusion that Jesus is magic, then we can assess this argument like any other. How the arguer came to believe the original premise p is not particularly relevant. What you call the “defeater critique”, I call the genetic fallacy.
It’s true that an interlocutor is never going to be particularly moved by an argument that starts from premises he doesn’t accept. Such is life.
The more interesting question is whether the arguer herself should be led to abandon her intuited judgments. But unless you offer some positive evidence for an alternative rational credence to place in p, it’s not clear that a “debunking” explanation of her current level of credence should, by itself, make any difference.
Think of intuitied judgments as priors. Someone might say, “There’s no special reason to think that your priors are well-calibrated.” And that may be true, but it doesn’t change what our priors are. We can’t start from anywhere but where we start.
It’s not unusual to count “thwarted aims” as a positive bad of death (as I’ve argued for myself in my paper Value Receptacles), which at least counts against replacing people with only slightly happier people (though still leaves open that it may be worthwhile to replace people with much happier people, if the extra happiness is sufficient to outweigh the harm of the first person’s thwarted ends).