In his introduction to the Robert Fagles translation of The Iliad, Bernard Knox tells us that in an epic filled with repeated shorthand descriptions—your "wine-dark sea" example, for instance, and Hector's "breaker of horses"—only Achilles gets "god-like." It is the "god-like"-edness duality of Achilles that makes Achilles such an arresting character, both in Elizabeth Cook's story and in Homer's. Both books are about force and violence and especially rage, all qualities shared by Achilles and the gods. Achilles, according to Cook, still rages even when he is dead.
Knox says that there are two human characters in The Iliad who are godlike, Helen and Achilles. She is the daughter of Zeus, and he is the son of a nymph. Both struggle between acting like gods and acting like humans. Both begin as completely self-absorbed, unconcerned with the consequences of their actions for others. Both are isolated—Helen by her beauty, Achilles by his rage and power. I like the way Cook portrays Helen's beauty as coming from a sort of Teflon quality with "perfect composure" that is "like a smooth wall which resists all impressions," and the way that beauty enrages those around her as they try unsuccessfully to mark her.
Look at Cook's description of the spear that Chiron makes for Achilles for a powerful metaphor about choice and fate. "The tree which made it was always meaning to become a spear." Yet Cook also explains that it began like any other and then was tended by Chiron to grow straight and unimpeded. She says it could have been something other than a tool of war. It was straight and tall enough to be a ship's mast, but Chiron cut it down with an ax whose handle came from an ancestor of the tree, and made it into a spear.
And look again at that opening description of the two rivers flowing in contrary directions, one filled with life, one anoxic. It is an image echoed in the description of the brain in the "Relay" chapter about Keats. Odysseus travels those rivers, and "the waters rope together to form a single cable" that pulls his boat to the edge of the ocean. Yet then the pulling stops, and "nothing helps or hinders Odysseus and his men as they row to shore." There is that extraordinary description of the rape of Thetis that turns her violation into his and then results in a relationship that lasts through the births of seven children. There is the literal rape of Troy, as warriors "see the mother's expression as you rape her with your hand, your penis, your spear, in the presence of her dead or dying child." This is explicitly tied to the soldiers' attempt to regain a feeling of power after all that has been taken from them. Again and again we see flickering variations on the themes of choice and control.
So, what is most arresting is the way that Achilles is marked by his experiences. His fate may be predetermined, but he shows a growth in understanding and compassion that moves him from the godlike to the human. Setting the standard for flawed and human heroes for millennia to come, Achilles may not be able to change his fate, but he can change his heart. In the context of the story's themes of destiny and inability to choose, that is an extraordinary moment.
After Achilles has killed Hector, he does his best to desecrate the body. But Hector's father, Priam, comes to see Achilles, humbling himself, to ask that the body be returned so that it can be properly buried. Remember what Antigone sacrificed under similar circumstances. As the two men look at each other, Achilles thinks of his father, and Priam thinks of his son. "The two men hold each other and weep: for those they have lost, for those who will lose them, for all the men gone down in the slow years of this wasteful war." Achilles, afraid that he will kill Priam if Priam attacks him for what he has done to Hector's body, holds himself back. He orders Hector's body be anointed. They eat together, and Achilles achieves what his triumph over Hector could not give him: a sense of peace.
And from this point on, Homer no longer calls Achilles "god-like."
Cook says: "Achilles is now more mortal than ever. Knowing this, he fights like a god and Zeus is as proud of him as if he'd seeded him."
My contribution to the relay is to respond to your question about violence with the beginning of Walt Whitman's "Leaves of Grass." As the poet prepares to undertake an epic and considers worthy subjects, he is addressed by a phantom:
Know'st thou not there is but one theme for ever-enduring bards?
And that is the theme of War, the fortune of battles,
The making of perfect soldiers.
As you said, the descriptions of carnage in the book are terrifying. The part you quoted about Thetis combing through the ashes for bits of Achilles' bones made me think of the people working at the World Trade Center.
The hope in telling these stories is that we, like Achilles, can learn patience and compassion. We can recognize the combative currents and someday soften the imperative to reach for the spear among the bracelets and dresses—or for the toy gun among the stuffed bunnies. We, like Achilles, have been "as good at dressing wounds as making them." Homer, Keats, Whitman, even Cook, help us to grope toward answers for the questions you pose, and they do that by illuminating the very things we might otherwise turn away from.