I can't figure out how to move my main character into another room by another means than an exit. The scenario is that a button becomes visible after a number of turns, the player presses it, which then runs the following script:

If: object is visible [object button]
Then: Print [a description of the floor dropping out and the character sliding down...]
Move object [player] to object [lower floor]

The description of the player sliding is printed, but the player does not move to the lower floor room. Is it not possible to move (transport) the player in this way?

That should work - that's exactly how you're meant to do it. It could be a simple problem. If you attach the game, I'm sure we can figure it out.