Is there a way (app, root code, etc) to set a different alarm sound for each alarm?
Hopefully this app is your answer: GM Alarm as mentioned in google play, this app has different alarm sounds and you can select the option for random alarm sounds each day. and the alarm sound will not repeat as it maintains a history for previous alarm sounds. Might be useful for you.
I think the best option is Sleep Bot. you can choose an alarm sound for each alarm, you can have plenty of alarms with different labels, you can also choose individually the snooze time.and the seconds you want the alarm to sound!!