Hi,
Well, I'm not sure what you mean then.
I just checked the situation on your website and I can see that you have the new add to cart system with the new add to cart buttons (which confirms that you've turned off the "add to cart legacy" setting. And I'm able to add the products to the cart, and the cart module is updating and I can access the checkout without problem.
So to me, everything looks fine now and the solution provided by Philippe seems to do the trick. So I'm not sure why you're saying that it still doesn't work.
Please double check. You might want to test on another browser and clear the cache of your website if you have any. Maybe you didn't see the changes because you had some caching and thus were seeing the pages generated before you changed the setting ?
If you can see reproduce the issue, please provide precise instructions.