What about maybe having the TARDIS vomiting up some random rooms/areas onto Stacy from a malfunction? Normally the TARDIS is only accessible to Doctors/their CR (it seems like to me) and that might be more open if it had random rooms or random locations scattered about Stacy's tiers. It could allow access to new/weird tech, not necessarily anything game-breaky and it wouldn't be as pressuring as having it only open in an event-type thing and being like "this is the only chance", which would exclude anyone who wasn't there for that event.

Also if it was possible, would it be possible to important borderline animate animate objects (AKA I've been playing the TARDIS as having a man-eating randomly attacking library and a friendly dumbwaiter, for example. Stuff like that).