1) A Cthugha story that doesn't revolve around fire or firemen.
Yoga.
Hatha and Sahaja yoga have practices intended to awaken kundalini, the coiled primal energy housed in the base of the spine, often visually represented as a serpent of fire. The idea is to provoke a state of extreme personal invigoration, vitality, bliss and transcendence.
In an obscure mythos-based tradition of yoga, one is not awakening an inherent force so much as preparing oneself to be host to an outside force. It's dressed up with good hippy-dippy nonsense about "awakening oneself to the cosmos" and so on, but basically it's about fooling rich white people into becoming hosts for fire vampires. DG gets involved when a series of bizarre crimes in TOWN X are carried out by people who then spontaneously catch fire and burn to death before they can be apprehended; these people were yoga students who had reached a high enough level to become host to a "kundalini being" - a fire vampire.
2) A Ithaqua story that doesn't revolve around storms, the North, or freezing blizzards/snow.
You know where's cold?
Space.Astrophysicists staring out into the cosmos are making an unsettling discovery; "cold spots" and the so-called 'super-void' that account for billions of light years worth of cosmos where there should be stars, should be heat - and there isn't. In the cosmic horror of Delta Green, these voids are a kind of life in and of themselves, living nothings, embodiments of entropic stasis; even after the stars come right and the old ones walk, these things will be waiting for their time to shine. Maybe the thing we call Ithaqa is an infant or degenerated version of one of these un-things, a small sentient eddy of heat-erasure.
These are philosophical, existential threats, so far and distant as to be not even actually "present" in the scenario; instead it's all to do with the nihilism their discovery creates in the DG friendly astrophysicist who goes to the Green Box and starts opening crates because why not, right? Sun'll swallow us before they do, nothing matters, etc etc.
3) Re: Shan. Make the Beings from Xiclotl (Shan tree like animal servitors) actually scary and totally distinct from Dark Young. Right now they are quite boring in a D&D sense.
This is a tricky one because a) as you say, they're very similar to Dark Young and b) they're so tied to the Shan that it's hard to do something with them that isn't ACTUALLY about the Shan.
I think one of the interesting things about the Mythos is the idea of Shoggoths and servitor races, these biological construct creatures. So what if, instead of being merely enslaved aliens the Xiclotl have a function, some biological reason the Shan keep them around other than for muscle?
My first thinking is terraforming; they're walking micro-climate generators that spit out toxic atmospheres that allow Shan to exist in their natural state without needing to hide in a human body. It makes them more interesting and bizarre, I think, and introduces more opportunity for bizarre descriptions instead of "it's like a tree but metallic".