Well, I come newly enlightened. And with good news-
Ranger, I don't think you forgot about this thread. At least, not completely.
Diving into the lore of Gorged on Ruins, I was struck by something I hadn't noticed before- the fact that the Voice of Rot is originally- or previously- from Drakr. There he (probably) served as lord to the Lost Riders, before being booted out and into Risur. I conclude that the phrase is meant to refer to the Voice's plan- to crawl through the Gyre towards Reida, the Plane of Time, and bring it and all the others to its end.
As for why it's scrawled on Cheshimox, and the Lich? I propose that the common thread is the presence of the undead. Cheshimox was from Drakr, and surrounded himself with ghouls. The Lich is undead and probably had undead followers. The Voice is the manifestation of Lanjyr's concept of Death- I suggest that undead have for centuries been picking up on the Voice's plan/prophecy. Sure, this long predates the Voice actually learning about the Ob's plan, but he's a fey titan who ends up wrapped around the Plane of Time- I don't think the normal rules of causality apply.
For some further reaching, one could point to the dwarven scrawling found in the Radical Eschatologist sewer hideout in book - "Arc white the lost world in the heart beyond the serpent shall gyre the end in the coils of ice". That line had long confused me, since the Eschatologists don't really know the Voice at that point. So, maybe it's a prophecy.... or, maybe it's related to the many nearby skeletons the dwarves reanimated?
All this is interesting enough- but I'd also like to point to something greater I realized as part of delving into this topic.
Reading ahead in the AP, I found myself a little underwhelmed by the Voice of Rot. He seems an uncomplicated villain- a big dumb white snake that wants to kill everything because to it, death tastes like candy. Compared to the nuanced and philosophical villain of Nicodemus, it seemed like no contest- one is a villain deeply embedded in history, the other is some big evil serpent whom the party doesn't even know is a villain until quite far in.
I was directed to my first realization by noting something surprising in Gorged on Ruins- the Voice is originally from Drakr. That was quite shocking to me, as I was given to understand that the titans were deeply tied to Risur specifically; after all, if not, why doesn't Ber have any? It led me to compare how the players' guide and Gorged describe the Voice, and I found the difference quite startling.
Player's Guide: The Voice is a fey titan. Controls swamps and dead animals.
Gorged: The Lost Riders seek the eye of their lord, the Speaker of Snow, Heart of Black Ice, and the Warden of the Bleak Gate- now called the Voice of Rot. With his gaze he could command the corpses of beasts and the souls of men. He is this world's manifestation of the very concept of death.
Thus, I realized- the Voice of Rot isn't just a fey titan. After having his eye ripped and being being brutally defeated by both 'Ancient Heroes' and King Kellend- that reduces him to being 'just a fey titan'. But as the AP gets underway and the Voice sees a chance, it is able to recover much of its ancient power- to become the entire world's manifestation of death, and to bring that death to the world. The AP 'lowballs' the titan's true puissance, to let it flower in later books, as a surprise to the PCs.
This led to my final realization- sparked by your citation of Russ Morrisey's words, in the forward to Act 3.
The conflict isn’t existential, but philosophical. One age is about to end, another set to begin, as foretold in the stars.
The Voice isn't a 'bad' philosophical threat, in competition with Nicodemus' layered and sophisticated philosophical threat. He is something else- an existential threat, providing a wonderful duality and a sense of completion to the end of the AP.
I still need to do a little thinking on what that actually means- how it impacts on my running of the campaign, what I present to my players and how.
I suppose I just wanted to say, for now- kudos. This AP is better than even its writers know- well, unless I'm just imagining things, heh.