For fire, other possible adjectives are unquenchable, incandescent, resplendent, or torrid.
For air, one could also use wild, squall, turbulent/turbulence, or sharp. I like Aryx's suggestions too, but it would be odd if wind and fire were all -ing words when none of the others have any.
Possibilities for earth, if you don’t like Edifice:
Node, Vein, Outcrop, Bastion (I kind of like vein just for the mental image of a grizzled dwarf miner. He removes his helmet, spits, and says to his supervisor “We’ve hit a Rich Vein of Elemental Earth down here. Gonna slow production, least if’n ye want us to go around it so ye can tap it later.”)
I also like outcrop for its meaning, but it doesn’t sound as cool, though its meaning fits perfectly (it’s defined as a place where bare rock is visible on the surface of the Earth).
I like Bastion because it’s roughly synonymous with Edifice, but implies an inherent strength and power to it (in my opinion).
It has a somewhat specific shape implied, but perhaps Earth could be "Hedron". Alternatively, even though one might think of it as being more Air focused, perhaps "spire" ?
Earth is typically associated with strength and stability, hence "edifice". I also (for poetic reasons) liked having each of the names alliterate with the element - furnace of fire, aerie of air, wellspring of water, edifice of earth.
Earth is typically associated with strength and stability, hence "edifice". I also (for poetic reasons) liked having each of the names alliterate with the element - furnace of fire, aerie of air, wellspring of water, edifice of earth.
What about Monolith for earth? Barring that, I think bastion is my favorite, followed by vein. Edifice feels too flimsy just in terms of the way the word sounds; it's almost french! "Edifice a la Papillion"