(Sorry for a text wall, I'm very interested in the topic)
I'm unconvinced the game has a diegetic (edit: I'm not using this term quite right, in this case I mean 'diegetic' as in 'part of the world' as opposed to 'part of the game/text') narrator to begin with. It's certainly not the default assumption, and I can't think of any particularly compelling pieces of evidence to support it. Additionally, that you are convinced there must be multiple narrators instead of one, to me, implies convolution. To me, if there are lines of narration that have contradictory implications about the speaker's in-universe identity, then that's evidence that the narrator's identity is simply nondiegetic, because a nondiegetic narrator inherently has no in-universe contradictions.
Surely particularly notable lines of narration can reflect certain characters (though I can't think of any off the top of my head), but that doesn't mean that there is a consistent pattern to all narration; only that those particular lines reflect those characters (regardless of if there is any in-universe component, like Cthulu transmitting messages to Quote).
Speaking of though, if you do want to say there is a diegetic narrator, then how it works is handed to us on a silver platter: the narrator is transmitting messages to Quote. We know this is possible, because the first cutscene is a POV of Kazuma, which is explained by it being a transmission. A big convolution to me about Cave Story have a diegetic narrator is that it's not a particularly meta game outside of a few select fourth wall breaks. A diegetic narrator would be out of place in a story that is largely not meta (or doesn't have a good reason to have a diegetic narrator; think of stories that are told from the perspective of someone recounting events, for example), but if you were to bundle this into a larger, comprehensive theory that states that most things we see are diegetic, down to the hud for example, then it's much more compelling to me (even if the burden of proof gets much larger when proposing such a massive theory). What I'm getting at with this overlong paragraph is that it is possible (though unlikely in my opinion) that most cutscenes are reflective of what Quote is seeing (either in person or via transmission) and that the HUD is a part of Quote's vision (think Terminator), and bundle those together with this idea of a diegetic narrator.
As for the specific identities you propose, Cthulu makes senese, and Pixel is arguably the default assumption, but why the 'debug cat' in particular (and, who is this? the orange cat seen in the credits?)? Also, is the implication that Cthulu is based on one of Pixel's friends? Is Cthulu in the credits as someone in particular? Further, I'm wondering why the fourth wall breaker role would be different from the meta-narrator role - seems redundant to me; I see no reason to suspect these would be different. Additionally, the in-world-narrator role is strange to me too, because the example you gave is a gameplay tip - wouldn't this make more sense to be the fourth wall breaker or meta-narrator (so in my opinion, Pixel)?
Also, maybe this is what I should've led with, but you seem to count not only standard narration (text boxes with no in-universe speaker, like "Got the [item]!" or "The door is locked"), but also signs. This is narration technically, but in video game discussion generally that's not considered the same thing as 'narration', in my experience. Regardless, the issue here is that the signs are already known to be in-universe elements. Obviously King or Arthur or someone wrote "Welcome to Mimiga Town!" and "Resevoir" and the like. Santa wrote the sign in his house explaining instant death spikes. For more mysterious signs like "That's all, folks!", you'd presume that's Cthulu, Misery (of the three currently occupying the castle thing, she seems the most likely to write that sign), some other unexplained figure, or that there's no in-universe explanation at all and it's just a fun pseudo-easter-egg. What I'm getting at here is that the identities of the sign makers is effectively a different question from who the narrator(s) is(/are), since we already know the signs exist in-universe, and can make some educated guesses about the identities of certain sign writers.
Ultimately, my thoughts are this: there is one narrator, Pixel. For the most part, this narration is the standard video game narrator affair (albeit with a bit more personality than usual). This includes reading what is written on signs, informing the player about certain objects, explaining certain game mechanics, and giving boiler-plate narration ("You got the [item]!" and the like). It's possible that there are certain points where the narrator is lampshaded more than usual, or times where the narrator has a more direct in-universe presence, but I can't think of any, and I'm inclined to say that these instances should be regarded as stand-alone oddities rather than evidence that the whole of Cave Story's narration was written with the idea of a meaningful narrator in mind.
