4-1, 6-1, 7-1, and 8-2 only require the player to survive for a set amount of time, and there are no ways to end the levels early, so they shouldn't have categories.
On the other hand, I believe 9-1's leaderboard should be reinstated, as seeing who can perform the astronomically difficult 'Cutscene Skip,' commonly thought to be TAS-only, twice in a row would make for an exciting category.
After examining the assembly, I don't believe that skip trick to be a real thing unless there's some undeniable proof. The only moment at which either cutscene modes actually check if you're pressing Start is once the fade color is invisible.
MotDemoMainLoop (Loop for 3D cutscenes) is executed every frame so the cutscene can be updated as it's fading in, but it never reaches the check for "Start" at any point until the fade is complete and the cutscene switches to it's normal behavior state. Neither the state in which it's initialized or the "fade-in" state check for the input. And even if it was created in a state that let it check for it, it would immediately be overwritten by function calls afterwards before any frame of input can happen.
On 2D cutscenes, book_task_main can almost check for player input while it's fading in, since the assembly responsible of checking for input is reached if the book state isn't 1 or 2, and the fade-in state is 3... except, before anything, that check first sees if the book's state is 0, and since it's created at state 3 and it's only set to zero once the fade is complete you can't perform the skip in any frame before that.
As for the initial prologue cutscene being instantly skippable, that's because it runs on it's own code completely independently of the regular cutscene system used everywhere else in the game. opdemo_task only makes sure that you can't press Start to skip once it's already fading out, but neglects to check if it's fading in. That's why you can easily and consistently skip that even if it isn't done transitioning.