Time to explore the extended high region from about word 14,000 to 27,000.
The sharp increase comes right at the beginning of Chapter 3, A Short Rest. The end of the sudden decline, here:
[05.127] ‘Thief, thief, thief! Baggins! We hates it, we hates it, we hates it for ever!’
To use recognizable landmarks, all these unusual words occur in Rivendell, among the goblins, and with Gollum. We recall that unusual words are merely less-frequent, not high-register. This sustained peak includes Gollum’s sibilant speech and the goblins’ “Clap! Snap! the black crack” poetry full of sound-play as well as the descriptions of Elrond’s sanctuary and his high speech and Thorin’s and Gandalf’s responses in kind. Elves and goblins have their own languages and Gollum his own idiolect. I believe that these unusual words twist our ears a little, knock us off of solid, prosy footing. The slightly uncommon words are consistently so – enough to suggest the alien languages underlying these characters and places.