I'm unsure if this has been discussed before, but I was able to figure out how to warp Hat Girl around. In the first video, you'll see an example of just how far you are able to go.

You can tell that the elevator and the UFO are non-warpable so it brings me back up to the attic once I dive into the corner. In the second video, I show how some surfaces are 'warpable' and some are 'non-warpable'.

For some reason, when you dive into that corner at the right angle, it will warp you back into warpable surfaces. If the last spot you touched before diving was a non-warpable surface, it will return you to the previous warpable surface. I'm unsure if this can be done on other corners as this one was the easiest to replicate and the ledge its on is consider non-warpable.

This looks pretty much like Pepperoni Pizza, or what people call "stuckwarps" nowadays. That has to do with you confusing the engine into thinking you're stuck, and thus warps you to the last save spot.

It's a strat that is used in "Heating up Mafia Town" in the current route