Helping swimmers overcome a crossover in backstroke is a pretty standard job of coaches. Here's a quick progression that helps some swimmers.

Why do it:
Starting the pull directly above the shoulder is much more productive than starting it across the head.

How to do it:
1) First, do some kicking with your hands down to your side, working on your balance and rotation. Setting up the foundation of the stroke at the beginning of the progression means you won't need your hands to balance or leverage into this position.
2) Make sure you're rotating the shoulders out of the water each time.
3) Now do some kicking with each arm extended. Be careful to keep the hand just outside the shoulder. Try not to stack this too much... be aware of where the hand is.
4) Swim backstroke, focusing on keeping the hands above the shoulders.

How to do it really well (the fine points):
Feel wide. If you're having trouble with crossing over, making sure the hands "feel" wider than you think they should will help. While kicking in the extended position, make sure you feel the hand is ready to catch... that will be close to your starting point when you swim.