I think your missing that the Castle literally has a preexisting room that will open a door to Washu's lab because someone wants it to... a room that will move itself around if someone wants it bad enough. Its call the room of requirements.
Washu will/has except(ed) magic as something she can/has studied with Science!!! Washu doesn't have those arrogant notations that understanding how magic does something makes it no longer magic, but science. She gets that science and Science!!! are processes and mind sets not some kind of all consuming blob of nomming doom. Magic is a force/form of energy manipulation that can be studied... not something that needs to be uncreated... by somehow explaining its the result of string theory that somehow works even if we don't understand string theory and can't prove it it negates the concept of magic and therefore is a better idea to believe in.
Anyway, The Master Key is a wand. Its just one for channeling divine magic and not arcane.
Washu will/has except(ed) magic as something she can/has studied with Science!!! Washu doesn't have those arrogant notations that understanding how magic does something makes it no longer magic, but science. She gets that science and Science!!! are processes and mind sets not some kind of all consuming blob of nomming doom. Magic is a force/form of energy manipulation that can be studied... not something that needs to be uncreated... by somehow explaining its the result of string theory that somehow works even if we don't understand string theory and can't prove it it negates the concept of magic and therefore is a better idea to believe in.
Anyway, The Master Key is a wand. Its just one for channeling divine magic and not arcane.