I like how the mood more or less rises consistently from start to end.

I'd say maybe be more deliberate about- / experiment more with rhythm. For example, the last line of the first verse > Desperately in need for the nice breeze

feels a bit jammed into the rhythm of the previous lines. Same with the second line of second verse. This can be totally ok and even great if done deliberately, to highlight something about what the line is saying, sort of how a long galloping-sounding sentence can emphasise movement.

Also, every line being a new clause gets (semantically) repetitive and limits what you can do with rhythm, try some enjambments.

A useful method I sometimes use is to start a poem conforming to a specific metrical structure (like using only iambs, only n stressed syllables, etc.) then as I start to hear the poem better I let myself break the structure where it feels right. YMMV but this usually helps when I don't have a clear aural picture of what I want to say.

Hope this was useful!

Edits for formatting space between lines.

Along a cliff of blackened rock arises
Blackened cracks. Blistered stone splits wide
Exhaling breath afoul with bile; the putrid
Air is warm, and further in the cracks grows thick
And gastric hot

Inside the darkness: boiling heat and
Distant crackles; a deep inhuman moan
Cuts through abyss, along its back it
Carries demon screams and guffs of
Charring flesh

A sudden drop, into infernal black:
Observe the winding tributary, onyx
Flame flowing like silk and bathing all
In lightless heat. Perched atop the lapping tongues
Behold Old Charon's seat

Blackened robes that never seem to burn
A crooked figure built of igneous bone
That towers, still as stone, and still it would
Remain until the end of time, but for
Lord Hades' order: Plough the River Styx