In the details page you posted it looks like the size is bound to the cart column correctly. If you can verify that the item id is being added to the cart along with the other details this size should also be added to the cart.
You mention that you have the dynamic selection working on the cart but the value is not being carried over. Please explain this a little more so I can have a better understanding of what is occurring. Also do you have a link where this can be seen live? You mentioned going through the directions, which guide or how to are you using?