August Derleth was an Accidental Genius

Think about it. The neat, overly-tidy cosmology that doesn't quite make sense. The leaps in logic required to fit elements into an organizational schema that can’t support them. The reduction of complex natural systems into humanocentric moral binaries. The constriction of a vast and unknown cosmos into a well-delineated puzzle box where every component is named, categorized, and understood. Inventing components whole cloth to make the components work within a pre-existing framework.

This is absolutely how a lot of people would respond to the Mythos in-universe. You can’t tell me that Aristotle wouldn’t just declare that Hastur was obviously affiliated with the element of air - of course he would! That was his entire deal! And people would be citing him as fact thousands of years later despite him being obviously, demonstrably wrong!

HPL was writing the initial reactionary knee-jerk - people fearfully retreating from what they don’t understand and throwing up whatever ad hoc defensive rationalizations they can: “This thing is bad and gross and I don’t like it.” Then Derleth comes in and takes that original revulsion and directionless lashing out and forces it into a well-behaved and formalized shape that aligns with more formalized pre-existing notions. It's no more truthful than the knee jerk, but this is what human beings do when confronted with the unknown: We freak out, and then we start labeling and categorizing and rationalizing and trying to make sense of it all. Horror is a living thing.

To my knowledge (this is the part where I admit that my knowledge of Derleth comes second-hand - of the main expanded Mythos authors his still largely under copyright and less accessible outside of game materials) there's no sign of a rugpull. Someone would have pointed out if there was a moment in his stories where the trappings of elemental affinities and Great Old One family trees are torn away and it's revealed that these are inadequate human constructions pasted sloppily over an unknown and unknowable truth. Standard issue cosmic horror plot. But that doesn't happen, so unless he is a significantly more subtle author than he's given credit for he stumbled right into some prime as-above-so-below metafiction where the act of writing those stories and making those changes in reality mirrors the developments that would occur in-universe. 

All this in mind, the Derleth elements of the Mythos suddenly become extremely useful because you can use them to represent what people believe, rather than what's actually true. Lovercraftiana fucks up this step all the time, treating the Necromomicon or whatever the grimoire du jour is as the accurate and infallible truth when the much more interesting option is that it is a human-made text with human-made limitations. If you're writing about the unknown, you need to lean into that information gap between the things you know vs the things you believe vs things you don't know and can't know. (I've spoken about this before.) 

Bringing it back home - let’s take his goofy good vs evil Aristotelian element great old ones and make it an in-universe thing. Just going to do a sketch for now.

The Great Circle

A Greek philosophical school of the late Classical period, lasting for several centuries further before it was ousted / assimilated by Christianity. It is the first systematic attempt to incorporate the Mythos into existing traditions in the Mediterranean and served as the basis for Mythos cults throughout Europe and the Islamic world up through the early modern period; its influence is still felt within modern Scientific, Theosophic, and Spiritist Mythosism, though these movements tend to syncretize a great deal more material from southern and eastern Asian schools of thought. 

(As an aside; modern scholarly consensus is that the Byzantine suppression of Abd al-Hazra's Kitab al-Layl was fueled in large part because its sudden popularity was a threat to the entrenched and politically influential Great Circle.)

A brief overview of Great Circle thought:

• The cosmos was dreamed into being by Logos (Yog-Sothoth), who divided Chaos (Azathoth) into the four interacting elements of air, water, earth, and fire. Two groups of gods are created to adjudicate and sustain the cosmic order - one to maintain the heavens (the Elder Gods), one to maintain the material world (the Great Old Ones)
• War breaks out among the gods (Instigated by Nyarlathotep) as the Great Old Ones (and a small number of traitor Elder Gods) attempt to assume control of the cosmos and reshape it according to their own designs, contrary to the Logos. 
• This war ends in pyrrhic victory for the Logos-aligned Elder Gods; the Great Old Ones are imprisoned on Earth, the traitor Elders are banished to the Outer Darkness (and now called the Outer Gods), but the surviving Elder Gods are diminished in strength and retreat to the heavens (embodying themselves as the stars and planets) to recuperate.
• The Olympian gods and any deities claimed under the interpretatio graeca are inhabitants of human dreams and servants of the Elder Gods. They serve as the primary intermediaries between humanity and the divine powers.
• The Great Old Ones, while defeated and imprisoned, are not destroyed; with the Elder Gods returned to the heavens the Great Olds Ones still have significant influence on the Earth and still seek to enslave and destroy humanity; their many servants are forever attempting to free them.
• The incarnation of / son of the Logos appeared on Earth to save humanity from the Great Old Ones, but was killed by their servants. His return will instigate the conclusion of the war in the heavens, where the Great Old Ones will be destroyed and the rule of the Logos and the Elder Gods over earth will be renewed.

I think I might have undermined my own point here, because this came out way cooler than I had planned. Still, point remains - all you have to do is pick a key point or two (I usually aim for "okay, what's the dumbest shit in this story) and go "how is this belief false, and what terrible consequences come about because people believe it?"

For this setup, my first instinct would be to undermine the idea that the Elder Gods / Outer Gods / Great Old Ones are separate factions or types of entities to begin with, and definitely that the Elder Gods are in any way less dangerous to humanity. Or play up the idea that Earth is just a environmental casualty of their war - a bird's nest along the Somme. Two factions of incalcuable power, duking it out for reasons impossible to understand, for stakes you don't know, fucking up your planet just because it was vaguely in the way. Or play up the cargo cult aspect: Rilyeh is just a forward base in an interstellar war, no different from Allied forces building airbases in Melanesia and then packing up and moving on when its no longer needed.

Yeah I think I cooked way harder than I needed to on this one.