I'm going to play devil's advocate here if you'll indulge me, as I cannot really overcome my bias against blood echoes. The first point I want to make is that Rom's defeat is a game state trigger for a metric ton of things. The Doll's voice line being just one of them, I don't know that we can necessarily say that it is directly aimed at making commentary on Rom's blood echoes. It's easily imaginable that the designers figured "Okay, it's the halfway point in the game, player probably has a bunch of blood echoes by now. Seems appropriate to put the line in here", and they used Rom's death as the trigger to make it appear. In other words, the Doll doesn't so much say it in response to Rom's death as she does to the passage of time that has elapsed so far. To support my point, I would also point toward how killing Gascoigne makes the sun descend, and how killing Amelia turns dusk into night. Surely nobody would argue that it is their deaths that caused this, but simply a gameplay contrivance to advance the time of day in relation to the player's progress in the game. In a similar vein, I think Rom's death is simply the trigger for a bunch of new things in the game. Maybe I'm selling From short but for all their genius in world building, I think they frequently do make gameplay concessions; Souls titles are not story-driven games, so I feel that much of the things we are presented with have to be taken with a grain of salt. I also wonder what the line is like in the original Japanese script, and whether it would have a different implication.

Second, I'm not sure why you conclude (or posit the theory) that all blood echoes represent the lingering will of the great ones. While it is certainly plausible that a trace of their will would be present in anyone treated with the old blood since it is literally the blood of the old ones being injected into you, I don't see why we should discredit the wills of the dying. Both the Jap and English descriptions for Echoes, which you quoted, to me sound a lot like they are implying that the dying wishes of a recently deceased linger on for a while, like a ghost. Ghosts too are often said to linger in the mortal world because there is some unfinished business they left behind, so the comparison is really apt. Moreover, I also don't think the theory holds water because some of the things we kill, I find doubtful that there is even any connection to great ones. For instance, take wild animals - dogs and crows. I find it a bit difficult to imagine that they have all been treated with blood ministration, and I'm not sure how else they would have "acquired" ancient blood echoes otherwise.

That said, I like the link you establish at the end, that it is something in people's veins that drives them mad during the blood moon, and not just the mere closeness of the moon (which is definitely coming nearer) and a weakening of the barrier between worlds. I also like that it would soothe the doll, while driving others insane. Also worth pointing out that the song Winter Lanterns (whose ties to the Doll are undeniable) sing is pretty "soothing" if you listen to it, and we all know what happens when you are exposed to them.