The closest we can come to assessing the authorial tone here is to look at the narrator's tone – this is reasonable, since the author makes no judgments on his narrator and may in fact be the narrator himself.
Right, so about that narrator: he manages to somehow be ironic and self-mocking at the same time. In other words, he almost mocks his own irony. Check out our discussion of "Writing Style" where we talk about Hawthorne's use of the words "festooned" and "besprinkled" in the third paragraph. On level #1, these words are genuinely describing Dr. Heidegger's creepy study. On level #2, they are ironic, because the narrator is toying with theatricality in deceiving you, the reader, to believe his fiction – just like Dr. Heidegger uses theatricality to deceive his guests into thinking they are drinking the elixir of life (in one interpretation, anyway). But on level #3, the narrator is mocking his own exaggerated manner – sure, he wants to get his point across about the study, but does he really need to use words like "festooned" to do it? He's gone a little bit too far, and we think he recognizes this.
Of course, behind all the showmanship is Hawthorne's serious lesson: humans are fools, and in all likelihood will always be fools. "Dr. Heidegger's Experiment" is at heart a moral parable (see "Genre"), so we can't escape without a didactic aphorism or two from Dad. Er, from Hawthorne.