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

I know this is an old question, but since I have been recently looking up the 'how to's' of ciabatta (which is how I came upon this question) I thought I'd pass on what I've picked up through recent reading and practice.

Stretching the loaf out long-ways is an important stage of shaping a ciabatta, it seems. I imagine that everyone finds that the middle tends to be fatter when yo finish basic shaping, that's just the nature of trying to gather any flowing material into a stable form.

So, carry out the shaping to the stage you have it - but possibly leaving the whole thing a little wider and shorter to start with, but then quite firmly but gently, lift the dough in the middle and ease it out first to one end then the other, until the middle has thinned down and you have a slightly more strap-like shape.

Remember that the bread was invented as an Italian response to the domination of French baguettes in the sandwich market, so it does belong to be a distinctly long and narrow loaf, even if slightly less so than a baguette.

My neighborhood Italian baker sometimes over conpensates and the ends are thicker than the middle, but I think she makes sure the ends have a little more meat than the middle before the proofing. The second proofing isn't that long only about half and hour to an hour, its a fairly flat bread like focaccia. Also, did you flip them right before putting them in the oven? It helps even out the second proofing.

Have never tried making ciabatta, only french and sourdough french loaves; believe the problem you are running into is the same as when I first started though. Also believe that ciabatta, like French bread, is a bread which is not kneaded or uses very little kneading, due to it's wonderful texture. I give credit to "Joy of Cooking" for the solution, paraphrased as I don't have the cookbook with me:

After the first rising, when ready to form loaves, turn out the dough for one loaf on a floured flat surface and pat it gently (this is very important, if the dough is over worked, the gluten will form the long strands which give the fine texture, which you probably don't want) into a rectangle of the length of the finished loaf. When it is to the length and breadth desired, and of a fairly uniform thickness, begin rolling the dough toward the center along the long edges, pinching or pressing as you roll to remove air pockets. When both sides have been rolled an meet in the middle, turn the loaf over onto the baking pan for the final rising and tuck and pinch the ends or turn them under or both and form the loaf.

A couple of additional things:

Make sure dough in the center of your rectangle is thick, as some of my loaves have split there when baking.

I make my dough as thick as reasonably possible, which help it keep it's shape.

I preheat the oven to hot, 230 C / 450 F before putting in the loaves, and turn it down to the suggested temperature immediately after closing the oven door, which really causes a good spring in the oven rising, and sets the skin fairly quickly, helping to hold shape. This technique is as close as I know of to using a stone to cook on.

Good luck!