mpoetess pointed this story out, A Slayer's Story. I now have to read the Chekhov story and re-read the parody again. May not be intended for all audiences, due to several blithe digs at Angel the series, Angel the character, and Boreanz the actor.
(I wanted to say "Boreanz... the, um, actor." But that would have been a gratuitous dig at a poorly timed moment and I'm only kidding anyway, I swear!)
I will now rec this and proceed to worry about who might hate me.
ETA: Chekhov's story is online and funny in its own right, though I'm not sure it's meant to be.