Sadly this seems to be impossible to solve with jquery… because I believe it is the cart cookie that is generated server side that holds this information.
Just like you can’t create a button that empties the whole cart with jquery (tried it and failed 
)… Or you can’t preselect a country in the checkout (The UI will tell you your JS / Jquery is working but the actual thing is not updating accordingly.).
All those seem to be linked to a cookie which holds the information and is updated when user navigates and shops.