On https://www.gnu.org/software/emacs/manual/html_node/emacs/Choosing-Modes.html, the manual says: "If the element has the form (regexp mode-function flag) and flag is non-nil, then after calling mode-function (if it is non-nil), Emacs discards the suffix that matched regexp and searches the list again for another match. This “recursive extension stripping” is used for files which have multiple extensions, and the “outer” extension hides the “inner” one that actually specifies the right mode. For example, backup files and GPG-encrypted files with .gpg extension use this feature."

My understanding of this paragraph is that the outside mode-function should be called, and then subsequent mode-functions should be called after. Currently, only the inner-most matched suffix has its mode-function called.

It looks like the (when mode (set-auto-mode-0 ...)) was moved from inside the (while name ...) to outside when the section was pulled into its own function. It's been four and a half years, so maybe it doesn't matter anymore, but if that's the case the manual should be updated; it would have saved me a couple hours of difficulty.