I haven't looked over all of the levels, or read all of the posts, but has this idea been attempted? Lovecraft's works are in the public domain (despite August Derleth's attempting to claim copyright), & at least Cthulhu is probably firmly entrenched in popular culture. So the only question really is does Cthulhu, Yog-Sothoth, Shub-Niggurath, Nyarlathotep, & the rest fit in with the mythology of the Backrooms?
How they could fit in is thusly: you have a number of godlike alien beings who (with one exception) are trapped in one level of the Backrooms, who have been trying for eons to return to Earth. Wanderers who happen to stumble into this level are at great risk of a psychotic break (aka permanent insanity), physical harm, death — or worse. (You really want to spend eternity as a living being in Hell?) Even the most powerful Backroom entities would not only avoid this level, but detour far away from any entrances to it. The only saving grace is that they consider other beings much the same way as we consider nemotodes or cockroaches: if they deign to notice them, it is to toy with them or kill them.
According to pop culture, Cthulhu alone makes Satan a regular Mother Teresa. And that's when this octopoid alien is in a good mood.
However, there are a few beings who did intentionally enter this level, & have survived the encounter with these monstrous beings. They remain in this level, incurably insane, acting as priests to indifferent gods. Although some kidnapped from this level have provided what little is known about this level.
As for a description, I'll point to Lovecraft's story, "The Call of Cthulhu", where he described this "nightmare corpse-city":
"Without knowing what Futurism is like, Johansson achieved something very close to it when he spoke of the city; for instead of describing any definite structure or building, he dwells only on broad impressions of vast angles and stone surfaces — surfaces too great to belong to any thing right or proper for this earth, and impious with horrible images and hieroglyphs. […] He had said that the geometry of the dream-place he saw was abnormal, non-Euclidean, and loathsomely redolent of spheres and dimensions apart from ours. Now a seaman felt the same thing whilst gazing at this terrible reality."
As I said, there would be one exception to these godlike aliens being confined to this Backroom level: Nyarlathotep. According to the Lovecraftian canon, he is the messenger of these creatures, so it is possible that he could return to the Frontrooms if the keepers of this Wiki agree; it would mean he is the only personage or entity who can do this. Not that this would be of benefit to anyone — probably not even to his fellow Great Old Ones. Dealing with Nyarlathotep is unimaginably dangerous: you'd be safer having meeting with Jeffrey Dahmer, John Wayne Gracy, the Green River Killer, & Jack the Ripper in a deserted stretch of road in the middle of nowhere. For example, if you were to agree to his terms to take a message to the Frontrooms, he may take it, or not take it, or deliver a different message, or lie to you about any response.
Yes, this would be Level 5 Deadzone — although not for the same reason other levels are rated so. Which means if the consensus is that there are too many Deadzones, that would be a good reason not to have a R'lyeh level. At least not as Lovecraft had envisioned it.