Moving shipping location on order review page

I am trying to move the shipping radio buttons into a separate table below the product order table in woocommerce, but for some reason every time I select a shipping method the page refreshes and then shows an extra ‘shipping and handling’ table below the one I just clicked in. If I click on another shipping method it adds yet another shipping and handling table. How can I stop that from happening so it shows just the one table?

It looks like ajax updates the product checkout table when I pick a shipping method, but in doing so it adds an extra ‘shipping and handling’ table because it is no longer part of the products table for some reason.

Here is the site I am talking about so you can see the behavior yourself : http://potenzmittel-verkauf.com/start/checkout-4/

https://wordpress.org/plugins/woocommerce/