It sounds like your body is scheduling your dreams for around 6:00. Try changing the timing of your WILD. Try scheduling it right in the middle, around 4:00. Do you normally remember any dreams from the time period between your two awakenings?

Also, let yourself drift off to sleep a bit more. It sounds like you are doing fine on the awareness front. You just need to actually fall asleep, like you are doing at 6:00.