What breaks the enchantment?

[Mister Underhill]

Let's do this true western style and just get a rope.

I grant that the 12 in 1 jury and judge is right in calling this nit-picking,

Actually, in all seriousness, I think you're going beyond nitpicking here and into an arbitrary division between what you term "narrator" and "conversational storyteller" styles. There's no formal rule or convention that I am familiar with which Tolkien has violated here. I can't see why Gandalf need reference either himself or his audience to sound authentic. Indeed, Gandalf's voice would soon become wooden and tiresomely pedantic if we corrected all of the exposition that he delivers to conform with this dubious "rule". Stow that baggage, mister! There's no reason why Gandalf can't "narrate" a story that he's recounting, even if he's a character in that story.

As has been pointed out on numerous occasions in the past, LotR is rife with stories (and a consciousness of storytelling) within the story -- which as far as I'm concerned makes Middle-earth more believable, not less.