which Splunk Version do you use? I am able to adjust the order of the App menue by drag and drop the apps in the launcher/home view (the tiles in the home screen).
So for me this also reorders the apps in the menue bar accordingly.
Edit: I searched a little bit and found that you are correct. I have a user-prefs entry that looks like this in my user folder:
appOrder = search,no_search_test,lookup_editor
But there might be a user-pref.conf in the user-prefs app and more user-prefs.confs in the splunk user folders. I guess to change this for all users, you have to change it in the user-prefs.conf in the user-pref app.