Bootup on lower power not functioning
So... turned out what was happening was all in code. Turns out that I was initializing an interrupt on INT0, when it was low, at the very beginning of my code. Problem was that when it started up on 3V backup power, INT0 was always low because INT0 is tied to the 5V line (it's how it knows to go to sleep). Because INT0 was low and the interrupt was triggering on low it was causing a constant interrupt to occur, never giving the rest of the program any time to run. Switched to enabling that interrupt only once I've entered full waking mode and it works fine now.