On a supernatural note, grace is what it takes. IMO, the Lord is pleased with effort and intentions when someone is trying something new at his leading. Peter Lord's wife wanted to do the same thing you did. She felt convicted and tried. She would wake up and then get her bible and sit down. When she sat down, she went to sleep. But the conviction was gone. Why? Because she was being obedient. She just didn't have her body trained yet.
On a practical note, He knows our flesh is weak and you are just now trying to train it. When we exercise, it takes time to get our bodies to do as we command them to do. We box, but not without aim. Your spirit will eventually bring your body under control. Keep making a go of it.
Also, go to bed at the same time each night. If you need 8 hours sleep, then go to bed early enough to wind down and give yourself time to fall asleep by 1030pm. That gives you a full 8 hours before time to get up. Don't do things in the evening that will excite your mind or body. Don't read an interesting book that will get your thoughts going, or do anything that might arouse your emotions in a passionate way (i.e. politics, news, ect.) The idea is to start calming down before bed.
Finally, get up at the same time each day. Your body will get use to the program after a while and start getting in line but it takes a while. Don't take naps.
Another thing to try, instead of starting out praying right away, perhaps it would be good to focus on buffeting your body initially. In other words, wake up and go for a long walk. Use that time of walking to pray. You won't fall asleep while walking. And your body will have the juices flowing so to speak. Then don't nap until bedtime. Believe me, if you keep a schedule, your body will adjust and you will become more of a morning person eventually. It's all about training our bodies.
"May the Lamb that was slain receive the just reward for His sufferings." A quote by Moravian missionary that sold himself (along with a friend) into slavery to reach those that the slave owner prevented from hearing the gospel.
May I live for Him and not for me.