Think about it – if you had some fetish or gross/weird habit and your parents found evidence of it and confronted you about it, would you admit your fetish/habit to them, or would you fiercely deny it? Of course he’s embarrassed and will fiercely deny everything, even in the face of irrefutable evidence.
I wouldn’t call panty theft “very illegal” (petty theft is a misdemeanor) or “predatory” – he’s not preying upon another person for sexual reasons (which is what sexual predation entails), just stealing panties (which is still definitely creepy and inappropriate and petty theft).
Look for a behavioral therapist with experience/specialization in sexual issues (check out the therapist search on the Psychology Today website) so he can have an understanding outlet for figuring himself out in this regard and deal with his behavioral issues stemming from it. It’s very possible he won’t cooperate (out of embarrassment/denial), but it’s worth a shot. And definitely stress that the issue is not what he’s doing privately in his bedroom that bothers you, it’s the thievery, and that if he wants you to leave him alone with his private activities forever, then he needs to leave your stuff alone forever (and get his own).