I work at night a couple days a week and when we were potty training my son my husband forgot to put a pull-up on him at night and sure enough he madeit through the night and went potty as soon as he woke up. It was like he realized that "safety net" wasn't there so he knew he couldn't go potty in his big boy underwear. It has now been 2 years since my son has been potty trained and we are lucky enough to have one had one accident!
So, we did the same thing with my daughter. We had planned to put her to bed without a pull-up after knowing that she had mastered the potty during the day. Believe it or not my husband forgot once again to put on the pull-up and once again it worked like a charm. She has been potty trained almost 2 years (my kids are only 11mos apart) and she has never had an accident!
My fried was having the same problem as you with her daughter - pull-up full to the brim in the morning. I told her my stories and she decided to try putting her to bed in big girl underwear. The first night she had a small accident, she woke up and yelled for mommy but not soon enought and she let out a little amount but then got to the potty to finish. The next night she made it through to morning - another success!
You might want to give it a try - it seems to work.