The opposite of a paean

Solution 1:

Given that a "paean" is a "song of triumph, praise" (see παιάν, sub II, and I'm aware that English isn't Greek!), my inclination would be to go with "lament" or "dirge" (a song of death or defeat).

If you wanted to reflect the opposite of "paean", there is a corresponding term in Greek, θρῆνος, which comes into English as a "threne". The most recent example in the OED is from 1960, R. Eberhart, Coll. Poems 1930–60, p. 14: "The perfect lament, and threne of sorrow's throat". As an adjective, you've got "threnetic" which might apply nicely to the dystopia you're writing about.

Fairly obscure, it has to be said, but that's not necessarily a bad thing.

Solution 2:

A jeremiad, from the Book of Jeremiah, is a lament and warning about the evils that are to come (because, as anyone over 35 knows, the world is going to the dogs).

A Philippic (from Cicero's speeches against one Philip) is a tirade of invective.