High Hydration Loaf Loses Shape on Baking Stone

Hi all.

This is my first post on TFL although I have admired the wisdom of many posters from a far for some time now. I started baking sourdough almost 9 months ago. I am consistently making a strong, basic sourdough loaf in my dutch oven. I am also making good baguettes and flatbreads.

Several weeks back I became a patron of the Philadelphia-based artisan bakery called EEVA. Well, their sourdough loaf blew me away. I have become obsessed with replicating their sourdough bread. I purchased a baking stone because it was more cost effective than the Challenger bread baking pan. I also purchased oval-shaped bannetons.

After overnight fermentation I did my normal pre-shape folds, shaped the loaves, and placed the loaves in the banneton. The loaves did not get much time in the refrigerator, but upon placing the loaves onto the sheet for scoring and pre-bake water sprays, the loaf began to run and lose its shape quickly. I decided to bake the loaves anyway even though they lost shape steadily. Predictably, the loaves turned out to be long and relatively flat. They lost the oval shape almost entirely.

How can I get my loaves to keep the oval shape while baking on a baking stone? Any advice is much appreciated.