I've been thinking about the idea that somehow the PT room, or whatever caused the phenomenon of the room, actually caused the retroactive springing-into-life of PT itself. Maybe there's some remarkable object of some kind, disguised as a knick-knack (?), in the room... it would have to be something that's also in the empty RT room... in a cupboard, possibly.
It's made of some special material or... insert clever history for item, here.
I'm thinking the object is so powerful it can bend time and space on a Big Bang scale, almost, and after someone placed it in this room, another reality was created emanating from the room. If you removed the object to a different room, perhaps that becomes the Room. The guest bathroom, say.
Make it stop whatever it's doing for long enough, then "re-activate" it, in the Room, or A room, and possibly it starts generating a completely different PT, and the last PT existence doesn't exist, and never did. The object alters space and time, so it can retroactively reshape reality.
I'm not imagining an SF-like "device", but a supernatural object. Maybe someone dug too deep in an archaeological dig, and came upon a substance at such a deep layer that it was some substance fundamental to the world's existence, and the universe's? Then someone was crazy enough to fashion it into a knick-knack, then a Collins bought it. And stuck it in that room, and forgot about it.
Somehow, it doesn't alter RT I guess, except by splitting its reality into two, so that's an effect, I guess. Too far-fetched that RT is safe?
I think it's a nice aspect of this story that the lives of all these people in PT are hanging by such a thread, and can be snuffed out retroactively any moment.