[T]he authors would seem to be pointing to both Heidegger and Melville as providing a potentially transfiguring vision of a new relationship to Being as the one to replace the Enlightenment rationalist relationship to Being. And they very well could be right, but their visions would have to catch on culture-wide to fully qualify, and I don't know if the authors' commitment to pluralism even allows for that possibility. Maybe it does. And while they don't say so, they msut see their own book as playing an articulating role for the Heideggerian/Melvillean vision. But they're not trying to convert anybody; they're just trying to make a case that looking at the world from their point of view allows for rich possibilities that offer a non-monotheistic alternative to nihilism.
They are phenomenologists, so their goal is to describe the phenomena, which means all the stuff that happens in human experience. And the phenomenon that most interests them is 'mood', which they want to argue is a non-subjective experience--it's something given by Being that we attune to if we are receptive to it. They refer to Heidegger's description of the gods as the "attuning ones". When the gods favor you, they attune you to aspects of Being that effect feeling states and shifts in consciousness. And the difference between the heroes, or a figure like Helen, is that when the gods 'shine' upon them they are overtaken by a mood that raises them above the normal grade of human to be themselves god-like. When the gods abandon them, as Athena does Odysseus, they are quite ordinary and usually screw things up.
Would MH approve of the pairing up with Melville??
Not sure. Was it Jan. who mentioned Rilke? Not to say greek klassix, Holderlin, etc. MelvilleSPeak seems quite different sort of Being (not that one has a handy Being-o-meter available) than MH. Tragic, christian, Amerikan. Moby Dick has some stirring passages IIRC--Ishmael in the crows nest-- but Capn Melville at times sounds a bit crackerbarrel-ish.
Joseph Conrad IMHE a profounder writer, and his prose dazzling, even if a bit trite (ie and Ho-wood has ripped him off for years). Like Heidegger, Conrad also had a certain...catholic perspective (lapsed at least) which most 'Merican writers lack--Dreyfus tends to secularize Heidegger, I believe--or is it 60s new age-ized--. We don't get the authentic Heidegger via Dreyfus's readings--we get MH, Dreyfussed (and does Hubie read greek (or latin, or even Deutsch?)?? Ich denke nicht.) He's a hustler, IMHE