Here is my idea. The guest rides in Mike's car. Through the street and into the factory where the scream is harnassed as energy. Then you can go a few different ways on the ride.
The Movie Way: Inside the factory, you drive by when Randall attempts to steal the child. As you escape to the apartment, the radio in the car says there is a manhunt for the kid. As the car pulls into the apartment there are helicopter noises, and spotlights searching the room with Sully and Mike trying to hide in Sully's closet. As the car drives into Sully's closet you come out the other end where all the doors are kept. There Randall comes after you, swerving through a few punny doors, there is Randall about to take the kid. The ride drops under Randall into Boo's flower door. She is now safe as you drive by Roz shredding the door, and Randall being aprehended. As the car makes toward the loading station, Mike opens Boo's door and as the car drives through to the loading area, you hear Boo's voice say "kitty".
The Fast Way: The ride speeds up here, not too fast, but faster than Snow White. So the car drives home and the radio says the kid is on the loose. You pull into Sully's apartment and there is the kid. All of a sudden the room begins to shake, and there are searchlights and helicopters in the window. The car pulls into Sully's room with Boo in her monster outfit. The car pulls into Sully's closet and you are driving into the MI entrance. But then things get bad, you are discovered. The car races down the hall and into a door while RAndall following. As the car comes out there are all the doors. Boo's passes by and the car quickly follows. And the same ending from going through the punny doors goes on.