Here's my excercise for getting your back straight, just for something to try.
When you are out riding next, try getting on your toeside and rolling forward onto the balls of your feet in a centered stance. Let your knees and hips natrually follow that movement, while keeping your shoulders relatively quiet, and you will tend to find your spine start to straighten out, or uncurve. (The guys/children's version I use is "push your hips out like you're peeing over a log and you don't want it to splash you.") But I like the subtle approach with the focus from the feet up.
On your heels, it's a bit tougher. Think about that feeling that you had with your hips on your toeside when you rolled forward and try to duplicate that. I find that to do this, start on a gradual slope and play with pushing your knees forward to un-edge the board in a heelside slip (again, try to keep your shoulders in the same spot, letting the rest of your body move naturally underneath them.) From the un-edged/knee forward position that you've created, use your toes to pull up the edge of the board without letting your butt move back. That'll put you in the position to give you the control to change edges without the full body movements that a curved spine forces.
Try it out and good luck!
Anyone feel free to pitch in if I left something out or mixed up a movements effects on the spine or something. Haha.