Do you work on the weekend? If not, then you could go to night meetings Friday and Saturday. You could also go to a meeting during the day on Sunday. So that's 2-3 meetings you could go to without messing up your sleep schedule.
I wake up at 5:30 am Mon-Fri for work, I go to AA meetings during the week which are usually from 8 - 9 or 7:30 - 9 and it is ok for me, I still get enough sleep, if I'm really tired I don't go and I go to bed early instead.