Hey Mike. I had a custom feature on my website that allowed people to ship to a post office, which was not tied into to woocommerce at all. I needed this feature to be able to toggle the correct shipping option.
So what I did was, upon my javascript event, i toggled the radio button and called the change trigger on the shipping radio buttons so that the endpoint update_checkout would be called via AJAX and update my order review. Thanks for your response.