The order of the apps show in left app sidebar is stored in user-prefs.conf file for each user profile at location $SPLUNK_HOME/etc/user/USERNAME/user-prefs/local folder. The attribute name is appOrder and available under [general] stanza.
You can programmatically add/update the file for each user profile with your default order.
So basically we're stuck with bash or a scripting language? No administrative UI to do this, correct?