Sure, there's also that. Frankly, I haven't given much thought to their otherworldly knowledge; it seems to me a candle against the sun.
The incompetent thespians often act on knowledge that their characters have no way of knowing, and, yes, this includes knowledge of their world. It also includes conclusions they drew after long thought during an intermission, and things which they told each other out of character, and things which are going on behind or above their character's heads.
I'm not quite sure of the mechanism. Here I must admit a weakness: I know enough of mindscapes to create, recognize, or escape from one, but exotic phantasms are no special focus of mine. I think the cursed adventurers - where "cursed adventurers" is a term expansive enough to contain any beings which have replaced the original team of four - share a mindscape, with the accelerated time property. (I neither know nor know of spells which could achieve this, but accelerated time mindscapes are well-attested in the rumours and wild ravings of adventurers, mad wizards, and holy men, and since there's no visible spell aura we know that this is not spellwork per se.) A mindscape would be trivially capable of forcing them to adopt the roles their alter-egos have adopted, but there is an oddity in how they shift their awareness back and forth from the phantasm and the waking world - or rather, an oddity in how they don't, instead taking the fruit of long thought while shucking the shell of experience, which makes me suspect that the curse may have somehow duplicated their minds and bewitched both copies in different ways.
There's a spell for entering mindscapes which I intend to cast after I've had a chance to prepare different spells, which should give us more information; we can send a summoned creature through first to see what happens to the minds and bodies of entrees and whether the door is traversible in both directions - assuming that this is a mindscape and not some other stranger thing.
Or, if rather than be responsible grown-ups we'd prefer the part of responsible children, we could condition our casting of mindscape door on the favorable results of a commune question. And, while we wait on the cleric to cast their borrowed spells, we could prestidigitate our lozenge thumbs to taste like mothers' milk. When I organize a commune, I'll see it added to the questions asked.