Quick thoughts on this:
It seems that en-NZ is not a chromium locale on its own (instead, it is aliased to en-GB in CheckAndResolveLocale).
However, enabling en-NZ in the UI will add it to the "accept_languages" pref (see TranslatePrefs::UpdateLanguageList), which will lead to en-NZ being sent in the Accept-Language header.
I guess that this might be what causes the desired date formatting effect?

Assigning to Matt for triage.

So it seems like we are incorrectly wiping the original values when they don't match a Chrome internal locale but instead we should keep them for sending up with request headers while using the best match for the app-specific locale.

This bug has an owner, thus, it's been triaged. Changing status to "assigned".