This is Part II of the cutscene pause glitch saga, which started with https://www.speedrun.com/cave_story_plus/thread/fy4lt .

Since then, I managed to find a Best Ending warp. However, there is a catch: The key part of the setup requires running Curly Story's normal ending cutscene, and I am reasonably confident that there is no other direct warp to the credits that works entirely in the main story mode. (More on that in the future.)

This wrong warp relies on a glitch that I'll call "TSC overflow". This glitch technically exists in all versions of Cave Story, but can only be triggered by attempting to run a nonexistent event number, which requires either modding the game (to change the map data) or a glitch similar to Cave Story 3D's inventory glitch or CS+ Switch's Core Escape glitch. The tl;dr of how it works is this: If you attempt to run an event number that's higher than any event in the current map's TSC, then the game will read to the end of the script (without finding the requested event), but instead of throwing an error or silently failing or whatever, the game will then start executing TSC beginning at that ending point, reading off the end of the script. What ends up happening, then? Well, the game uses a buffer to store the TSC for the current map, and that buffer isn't cleared when you load a new area or quit to the title screen. So, the TSC that gets executed during a TSC overflow will typically be some remnant of a previously loaded map's script, which in the TSC buffer didn't get fully overwritten by the current map's script. Using the Core Escape glitch, we can carry flag 4000 out of the Core room, which causes drowning to trigger event #1100 (which is high enough to cause a TSC overflow in most maps) instead of killing the player. By manipulating which areas we've loaded previously and drowning in certain strategic locations, we can warp to the final Best Ending cutscene (and also do many other cool things; more on that at a later time).

If that explanation didn't quite make sense to you, I wrote a painstakingly detailed description of everything that's happening to make this credits warp (and the Normal Ending warp, if you haven't seen that already) possible: https://pastebin.com/uB4eF8nt

Now, the setup has three main parts:

1. Core Escape: Use the cutscene pause glitch the same way as before (pausing the game after triggering cutscene skip, to hold the Core shutter open), and leave the room after the fight before your air runs out. Then save in Dark Place (instead of escaping all the way out to the Labyrinth like you'd do for the Normal Ending warp). (You'll need some form of flight in order to be able to make it up to the save point. If you don't have the Machine Gun or are not confident in your ability to keep the Machine Gun at Level 3, you can grab the Booster v0.8 beforehand without affecting any part of this setup.)
2. Labyrinth Escape: Perform a TSC overflow from Dark Place into the Mimiga Village script. To do that: First enter Mimiga Village by any means. The easiest way would be to load up another save file that's close to the village (or start a new one). Note, if your Core Escape save file is in Curly Story, you must load Curly Story's Mimiga Village here. Otherwise, feel free to mix-and-match main story vs. Curly Story, if you'd like :) . Once you're in the main village area, quit to the title screen and load back into your Dark Place save (where you performed the glitch). Then drown. (Do NOT open the inventory at any point during this step, otherwise you'll overflow into the inventory script instead!) You should be taken to either First Cave (if you loaded Mimiga Village in the main story) or Assembly Hall (if you loaded Mimiga Village in Curly Story).
3. Credits warp: Perform another TSC overflow, from First Cave into the "Fall" map: Start by saving in Start Point. Then run Curly Story's normal ending (this must be Curly Story!) by any means (the easiest way would be to have another Curly Story save file in the Prefab House, before Hell). Quit to the title screen any time after the island falls and the screen turns to black, but before the credits roll. Reload into Start Point, then head out into First Cave and drown there. (Again, don't open the inventory at any time, or you'll mess up the setup.) If you did all of this correctly, there'll be a brief pause, followed by a fade-in and then the final Best Ending cutscene dialogue ("Close! Such a narrow escape."), which will roll the Best Ending credits afterwards.

Here's a video where I demonstrate the above steps in their simplest form, in case you didn't feel like reading all of that:

Naturally, this opens up a discussion about how we should treat this on the leaderboards. Given that the Normal Ending warp got its own category, I would expect this new Best Ending warp to receive the same treatment (although I'm not sure if the Curly Story requirement will be problematic). That means we should decide the rules and timing of that category. My inclination is that because most games' speedruns (that aren't New Game+ runs) are typically supposed to start from scratch, we probably shouldn't allow the use of pre-made save files (like I did in the above video) for official Best Ending warp speedruns. This setup can, in fact, be performed entirely from scratch in a way that isn't dumb, by making the following modifications:

1. Core Escape: Same as usual, except you must play in Curly Story.
2. Labyrinth Escape: The step of entering Mimiga Village can be done either by starting a new (blank) Curly Story save file and playing up until Mimiga Village, or on the same save file by going back to the Core to drown (triggering the intended drowning cutscene), then playing the game as usual without saving (going through Waterway, etc.) until arriving back in Mimiga Village.
3. Credits warp: After saving in Start Point, the normal ending can be triggered by drowning in Bushlands (this triggers the breakdown cutscene).

Obligatory video demonstrating the Best Ending warp on a single save file:

The question, then, is whether we should allow the use of a second (blank) save slot for the Labyrinth Escape setup (which is faster, but doesn't feel as nice and self-contained, if that makes sense), or if we should require everything to be played on a single save file (so that you have to go through Waterway to get to Mimiga Village). I'm personally kind of torn here, so I'd love to hear other peoples' opinions on the matter.

Update: Although warping directly to Best Ending credits requires going through Curly Story, you can alternatively warp to Ballos without needing Curly Story, by going through the Sanctuary Time Attack challenge instead:

1. Perform Core Escape, then backtrack to Labyrinth I and save.
2. Go into the Sanctuary Time Attack challenge, and play until you reach Passage? (the room after defeating Heavy Press that the boss falls into).
3. Quit out of Passage?, reload into Labyrinth I, and drown. (Remember not to open the inventory.) This will warp you to Corridor (the passageway before Ballos). Defeat Ballos to get the Best Ending.

This technically also works in Curly Story, and it even warps you directly to Seal Chamber instead of the room before it, but be careful, because it will drop you directly above spikes!

If you decide to attempt this, keep in mind the following:

• You will probably want some form of flight while fighting Ballos. I would recommend picking up the Booster v0.8 beforehand, so that you don't have to rely on Machine Gun flight (and possibly de-leveling your Machine Gun, which would be very bad).
• You will not have Curly on your back to help you. If you want extra health before the fight, you can quit out of the Sanctuary TA starting area and drown in Labyrinth I to get infinite +26 Life Capsules.
• Do not enter the Statue Chamber. If you do, you'll exit out into the pre-Heavy Press version of Passage?, and you won't be able to access the Seal Chamber anymore.

Although this setup is much simpler than the credits warp, I don't think it will actually be faster, considering that you basically have to go through Hell, and fight Ballos without Curly, and possibly do another TSC overflow glitch to get a bunch of extra health before the fight in case you need it. Nevertheless, I felt that it was worth mentioning that this possibility does exist, for anybody that wants to try it.