Replaying through the beginning now on NG+, some of the notes are a little clearer.
The general sense that I am getting is that the game takes place within a communal dream, with additional paths to and from other dreams/nightmares, but because of the significance of dreams to communing with Elder Gods in the Lovecraft universe, the dream is still important and doesn't mean it's disposable. It's likely everyone in Yharnum experiences this on the Night of the Hunt.
The first vision we're granted after the man with bandaged eyes injects us with Yharnum blood is a werewolf emerging from a pool of blood, approaching, and then bursting into flames. After that, the Messengers come to claim you as a Hunter. The initial wolf may represent the inner human beast that's now corrupted with Yharnum's blood, and its approach is the sense of it taking over, which most fall victim to. But because you do not, you are fit to be a Hunter.
The game announces "Nightmare Ended" rather than "Prey Slaughtered" both for Mergo's Wet Nurse and Moon Presence kills, but Mergo's the normal/false result, while the Moon is the complete/true result. The other optional Celestial bosses are there for flavor and setting, and develop more about the Healing Church and other areas of Yharnum and its blood.
In the shortest route to the end, the only required bosses are Father Gascione; Vicar Amelia; Shadows of Yharnam; Rom, the Vacuous Spider; The One Reborn; Micolash, Host of the Nightmare; and Mergo's Wet Nurse. By only being exposed to the minimum amount of information through the game and not collecting enough Cords, it would seem that is sufficient to end the Night's Hunt. With your task complete, Gehrman offers to return you to reality, and refusal means the Moon keeps you in the dream world as his replacement. The Hunt is over either way, but the cycle is not broken.
To break/transcend the cycle, you have to collect the Cords and confront Paleblood. In the beginning in Iosefka's Clinic, the first thing the player encounters is a note that the only way to transcend the Hunt is to seek Paleblood. Much later, in the Lecture Hall (F2), there are two notes toward the end, with one being a simple "Three third cords," and the other being a note linking Paleblood to the Moon. By collecting the Cords and confronting the Moon, you ascend to godhood and end the Hunt.