Wow, I didn't realise the average was 7 minutes! I'm with you there on taking a LONG time to fall asleep. I'd be interested to hear what you find out about improving that time.

As far as the alarm clock goes you could get a cordless travel clock. I sometimes set four alarms on my phone: 4.5 hours / 6 hours / 7.5 hours and 9 hours (when it's time to get up). I found when I did that I had those time's in my head and was expecting to wake up, so after a day or two I'd wake up a few minutes before each alarm or after each REM cycle. A couple of weeks back I was consistently remembering 3 a night using this method (but I've been lazy recently)