Not real evidence, but another thing that I think strengthens the narrator theory for me anyway is this.
Image description: Four screenshots from Undertale, from the Undertale Text Project (link here).
The first two are from the boss fight against Asriel when he's transformed into the Angel of Death, his goat head with long horns atop a floating, legless, triangular body with long clawed hands in gloves and giant, rainbow-colored wings spread out that are shifting colors. Face scrunched up, he's wailing and shouting, "So, please… Stop doing this… And just let me win!!!"
The next two screenshots are from much earlier in the game: the first is in the tutorial fight against the Dummy in the Ruins, which the player has spared. The narration reads, "You won! You earned 0 XP and 0 gold." The final screenshot is from killing an enemy. The player is LV 4 and the narration reads, "You won! You earned 100 XP and 140 gold. Your LOVE has increased."
End description.
The whole game, the narrator has cheered us on most any time we win an encounter with a monster, whether we fought or spared. The only exception is when we beat the boss at the end of the area, again whether that is sparing or killing (eg Toriel, Papyrus) - there is no narration when a boss encounter has been won. The only exception ironically is if you spare the injured Flowey after the Photoshop Flowey fight: the narration simply says, "Flowey ran away." (If you kill him however, the narrator says nothing, as with the result of every other boss fight.)
(Tangent: The Doylist explanation for this is probably that these are the main characters and their words to us when defeated is supposed to be what sticks, so having the narration say "Yay, good job! You got this from that!" might break up the mood in a way Toby didn't want. The narration for "Flowey ran away" is used instead to drive home how pitiful he's become with his tearful reaction to the Mercy spam.)
It just feels like something Toby would do, ya know? Asriel, the antagonist, pleading with Chara, the narrator who's been letting us win the whole game, to let him win. And then, even though they were jabbering excitedly earlier in the fight, they stay silent and say nothing back to his pleas, perhaps because they know he's talking to the wrong person and won't be able to hear them anyway (Frisk is the one he's fighting, not them), or perhaps because they can't bring themself to say anything else after the flashbacks (the narrator does fall silent suddenly after the flashbacks; the reality of it all hitting home for Chara and choking them up?). And of course, with the narrator saying nothing back, Asriel then ends up "losing" as he cries and has his change of heart.
Thematically, it's just too cool that, along with everything else, it makes it really hard for me to believe that Toby didn't intend NarraChara.
It would also make sense as a game the two used to play and perhaps the reason Chara is so quick to start narrating everything for us. Asriel has his Absolute God of Hyperdeath character the narrator is quick to recognize and describe, after all, so it wouldn't surprise me if this was a game they played: Chara the DM describing the world and enemies around Asriel as he, the hero of the story, ventures forth and battles enemies. Drawing their stories, recording their games with the camera. Flowey, the one-time hero of the story, turned villain, wants to keep playing but can never hear their voice again. And Chara, now reduced to just their voice, never able to speak to their friend again and now fated to narrate the real-life, life-or-death adventures of strangers in different worlds (with the silver lining that they at least seem to enjoy Frisk's and Kris' company).
It's also interesting to consider in light of this from Chara themself.
Image description:
Six screenshots from Undertale, again courtesy of the Undertale Text Project, all from the scene at the end of the Kill All run where Chara speaks directly to the player. The first image is a choice the player has to "Erase" or "Do Not." After the player chooses Do Not, Chara says, "No...? Hmm... How curious. You must have misunderstood." And then, in all-caps with their smile still unchanged but their eyes turned hollow and black, they say, "Since when were you the one in control?"
End description.
The only time Chara, our otherwise plucky faithful narrator, won't let you win. They deny you winning in a much more brutal way than the sad silence they give Asriel on Pacifist, and should you do Pacifist again after this, they make sure to snatch that victory from you too.