Oh wow, this was waaaay easier than I thought with Neovim!
; ~/.config/nvim/queries/elixir/injections.scm
;; extends
(sigil
(sigil_name) @_sigil_name
(quoted_content) @injection.content
(#any-of? @_sigil_name "JS")
(#set! injection.language "javascript"))
Thanks for pointing me in the right direction.