I'm just a friendly TASer visiting
Regarding where the sphinx teleports you: This depends only on what question he asks. Once he has asked his question, the place you will be teleported to when you present him with the wrong item has been decided, and is not in any way affected by randomness. Here's a table of where you will be teleported depending on the question:
Skull: Red carpet hallway
Horseshoe: The room where you get the horseshoe and water
Mirror: Coffin room
Bellow: Library (with the glasses)
Broom: Troll bridge
Map: Globe room (with the bellow)
EDIT: I now tried your idea to be teleported to the coffin room, get the scepter, and then move on to the staff. This will of course require a route change to get the mirror instead of the map, but still: Not counting the extra time it will take to get the mirror instead of the map (perhaps 2 extra seconds at most). I found this route change to be (brace yourself) an amazing 6.3 seconds faster. All those screen transitions that are skipped sure makes up for it. So even if it takes, say, 2 seconds longer to get the mirror instead of the map, this route change will still be at least 4 seconds faster. Nice!
Skull: Red carpet hallway
Horseshoe: The room where you get the horseshoe and water
Mirror: Coffin room
Bellow: Library (with the glasses)
Broom: Troll bridge
Map: Globe room (with the bellow)
EDIT: I now tried your idea to be teleported to the coffin room, get the scepter, and then move on to the staff. This will of course require a route change to get the mirror instead of the map, but still: Not counting the extra time it will take to get the mirror instead of the map (perhaps 2 extra seconds at most). I found this route change to be (brace yourself) an amazing 6.3 seconds faster. All those screen transitions that are skipped sure makes up for it. So even if it takes, say, 2 seconds longer to get the mirror instead of the map, this route change will still be at least 4 seconds faster. Nice!