hello! spoke with javi about this recently and after some digging, I somewhat understand how this glitch works (but not necessarily how to make it consistent). basically, the portal to the next level is always active, even if it's not visible. in order to progress to the next level, though, you need to be in the portal and have the button pressed down.
if you move/jump in a certain way where the portal should be, you can trick the game into thinking you're still in the portal, even though you're not, so when you press the button, the game instantly plays the cutscene which transitions you to the next level.
i've attached a messy proof of concept video, using a minor mod i made to the game to tell me if i'm currently "in" the portal. plan on cleaning this up soon.
this is possible in every level with a button (i'm not even sure the jumping i'm doing is necessary, but it brings me in and out of the portal very quickly, which seems like a good way to trigger a collision-related glitch). i haven't recorded all of them since it's still very trial-and-error. besides level 6 and 13, this seems pretty useful If a consistent setup can be found, since you need to pass by the portal (or it's not too out of the way) for each of these levels.
re: level 17, walking into the portal and then wrapping from the right wall to the left one seem to guarantee that you are "in" the portal, likely because the game moves your character's position so quickly.
would be nice if, when looking at statistics, there was a way to select only one record, and hide all others from the view. right now as far as i can tell you can only add/remove records from the view by selecting a category, and all are selected by default.