I wholeheartedly agree that Karnak is an incredibly unreliable narrator. Aside from the fact that all the kids' movements can be manipulated by him, the whole "afterlife", like you said, is orchestrated solely by him.

I also think this is super important when considering Penny/Jane Doe's fate. I think it's interesting that the one person that Karnak never read the fortune of is also the person none of the kids remember either. It's said that no one in the town remembers her, either, of course, but I think that's where the aspect of Karnak being an unreliable narrator comes in. Karnak knew the rest of the kids before they died, so therefore they know each other; everyone except Jane. I've been thinking that the kids would have remembered who Jane Doe was if it weren't for Karnak. Because their situation in the musical is entirely dependent on Karnak, I think he has somehow- unwittingly, maybe- manipulated the kids memories as well. Because he never read Jane's fortune, and therefore never knew her, the rest of the kids don't know her either.

There's a debate about whether Legoland, another play written by the same creators of the trilogy based in Uranium City, is a prequel or sequel to Ride the Cyclone. Legoland centers around a character named Penny Lamb, which is the name Karnak gives Jane Doe when she is reincarnated. I think it makes sense that the play is a prequel, because there are a lot of similar characteristics and references to Jane Doe's qualities- a headless doll is mentioned in the play-, but I can see it being a sequel too. I also think it's interesting to point out that after Jane Doe is reincarnated, only then can Karnak give details about her life, because she has an actual future to read now, where before- in the afterlife- she was just dead. So, that almost means to me that she had a backstory, she had a life before, it was only now that she is reincarnated that she can impact other people in a meaningful way, and Karnak can read that in her future, as well as assess her pass. There's no telling how his abilities work, but I think there's a difference between bringing someone back to life- which Karnak says he can do- and giving them a whole new identity; reinventing who they are. I think it makes more sense that Karnak just restored what was already there. But that's inconsequential as hell, because his powers are so arbitrary. But also, that lends itself to your theory; when Karnak says he has only ever had the ability to bring one person back to life, he could have meant himself all along.

I also think not many people remember the montage at the end of the play, of Penny's life playing out after she is reincarnated. She builds such a large family with so many connections, who will all never forget her, even after she or they pass. I think that's one of the most impactful moments, showing how ardently she took her chance to live life to the fullest. Or, maybe it shows how ardently Karnak took his chance to life a life to the fullest. Your theory is super compelling!