Correction:
Half five o'clock in the morning where she is so unless there's been some sort of emergency I imagine that she's asleep.
Should be a past there.
I do believe this is the most red I have ever seen out of Paul in an update; possibly in the entire fic.
And that's a writer who's quite thoroughly fucked. Literally his best bet is having the law throw the book at him, and hope that the Muses and their allies consider it enough.
The Greek Pantheon is not known for it's kind and forgiving ways.
And the guy who sold her to Madoc is screwed as well, for kidnapping and illegal confinement; if he's dead, he just falls into Hades' tender mercies.
And you can be sure they'd put in a word with other divinities if he ended up in a different afterlife.
Not knowing literally anything about the muse in question other than that they are divine and female, I'm really not seeing any way for him to plausibly explain how he found a single person out of billions that quickly.
Multiple plausible explanations:
Muses are distinctive; a hypertech supercomputer cross-searching inspired/successful works of fiction in the period of time since Calliope went missing would have generated a list of possible suspects to follow up on.
Or his Ophidian Eyes trick grabbed a lot of info, and the mention of Calliope's name jogged a memory.
Or his Quintessence scan while looking for Lex's servers detected her, but he didn't know she was missing.
I do expect him to simply fall back on Power rings are awesome, though; simple, and an old excuse.
Basically, he's been cultivating a reputation for competence for so long that no one is likely to ask how he did it, just that he did.
Reputations are good for that.