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.