I'm at the last stage, and I discovered that if pressing "A" at any point you have upward velocity without ever jumping (via glitch, or some other way) then you can slow yourself down, allowing you to fall sooner. This saves time in at least rooms; 0x11? on stage 1, the room with the 2nd clue in stage 2, and the room with the 2nd clue in stage 3. It doesn't sync with the current RNG, so just placing this here in case I ever redo the run.
Edit: For future reference
This section is extremely strict on the positioning. While the stairs clip works for both Scooby and Shaggy, if the speed and position of whomever you're trying to clip is off from the numbers shown by just a hundred or so, you get either ejected out of the stairs next frame, or get stuck.
The format displayed is X, Y, Speed X, Speed Y.