Honestly, your best bet is to log in during the morning (if you so happen to live in PST/CT/EST time in the US) and create a character then. It still works for Balmung from what I believe.
Even if you have to wake up early as hell to do it, you can still knock it out and then go back to sleep.
Even if you have to wake up early as hell to do it, you can still knock it out and then go back to sleep.