I was going to recommend sleepytime[1] to try and find a good time to go to bed at if you want to get up at 6AM. It looks like 10:30 is a good time though. Maybe try to find your sleep cycles and set your alarm for a time when you are not in deep sleep? There are some smartphone apps that are meant to help do this.

[1] http://sleepyti.me/

You can check [1] Sleep Cycle.

I'm using it mainly to track my sleep quality and to see my sleep patterns, but the app can wake you up when you're in the lightest sleep phase.

Unfortunately, I didn't use it extensively, so I can't give you adequate opinion on the wake-up function, but it's worth the try.

[1] http://www.sleepcycle.com

There's alarm apps that will let you set your alarm based on sleep cycles. If that doesn't work, you can try various sleep measurement devices to wake you up at the right time.

I miss my WakeMate!