Whoo boy. Well, the Rat King showed up, so what we do here is probably gonna be under a lot of scrutiny. Either way, I think we have a decent chance at solving it here and now- If Distortion Detective is anything to go by, there's a "percussive therapy" part to solving a Distortion (beating the crap out of it) followed by emotional logistics to eliminate the root cause. Hell, someone even manifested EGO that way. Right now we've given the Eternal Persistence enough pause- we can take advantage of its mental state now.
Sure is a good thing we're in control of a guy who specializes in unification of viewpoints and mental states, has experiences in Distortions (debatably even as members of Turb Office depending on how you interpret Memento), and has a pretty good amount of experience in herding cats in a general direction, eh?
[X] Speak to it.
-[X] "Is this really how you want to go Capone? Like some sort of starved, wild animal that just eats, shits, and sleeps until it can't anymore? That isn't a way to live, not when it's the same drive that convinced a father that two kids should kill a grown man."