In the game it's possible to warp from level 5-2 to 6-1 by doing a series of inputs that takes you to a fantasy zone. Up until now it hasn't been used in runs before, but since the info for it can be derived from hints in the manual, I decided to allow it from now on.

For those unfamiliar with how it works: in order to activate the warp you have to grab the last coconut on the ground just before the exit gem. While holding it, press Up, Down, L, Down, L, R, and R. In the fantasy zone, grab the rock. Make sure you don't destroy it!

Keep in mind you only have one chance to try it - in the case of a mistake you either take a death or continue on to 5-3 etc.

Okay, so important update here: @FinnKaenbyou discovered that you don't need to grab the coconut in order to pull off the warp! You can destroy it and perform the same inputs while being in the position where you'd normally stand. Keep in mind that you still have to press and hold down Y throughout the process, the same action you do when getting the coconut.

This definitely makes the warp a lot more consistent.

UPDATE 12/18: And on top of that, if you happen to destroy the rock in the fantasy zone, you can still warp! Just hold down Y when you're standing in the required position!