Rather than falling over and over to progress through days faster, or visiting all locations, for me personally something else would be a lot more interesting as it captures the essence of the game better in my opinion. How about going for the fastest "100 Dynamic Links" (or any other set number) instead of days? By Dynamic Link, i mean touching any of the objects (or sometimes events such as zeppelin landing, or getting shot, or the devil appearing) that instantly warp you without having to walk into it continuously. The gate to the Black Space would need to be banned from counting, obviously, but everything else should work fine. Ending a dream with a special event could also be awarded with a point.

Edit: In case anyone likes the idea enough, maybe "Instant Warps" would be a more accurate description for the category.

Is using multiple skill sets allowed? They can be changed quickly with F1-9 on PC.