Even though I have made my shipping costs 0 in my pricing structure, it still shows up and gets added to the price at checkout.
Has this issue been resolved in 3.1.3?
if, it is a shippable item the shipping cost will show, but setting one of your shipping option to 0 should do the trick also make sure that the first item is the 0 item on your list.
Also the user should be able to select and shipping option and update the cart.