how to get a ciabatta with a more uniform shape
Here's why I think this is happening:
In the oven, the internal temperature of the bread is going to transition from room temperature to cooked.  The only way heat it introduced into the bread is at the surface.  The sides have significantly more surface area than the center.  The problem you are having is the sides are making this transition way before the center is.  So the sides have very little time to rise and get cooked while the middle is in the prime rising temperature.  So the yeast in the center has substantially longer to work before it is too hot for it.

You can try forming the bread thinner toward the center and thicker toward the edges.  If you get the thickness right, it should be uniform.

I have also had good experience cooking on a stone.  It will almost certainly speed up cooking time, but should help keep the temperature transition uniform across the whole loaf.  So you don't end up with a thick part and a thin part; if you start out with a uniform thickness, you end up with a uniform thickness