Hotfix - Ok, we didn't get that quite right:
Fix cfw_get_shipping_total()
Essentially invert logic of cfw_get_shipping_total() so that it follows the logic of WooCommerce's cart/cart-shipping.php template by first checking the available methods, and then descending into other checks.
This also requires changing how cfw_show_shipping_total() determines whether to show the shipping total. Since error states are part of the shipping total, those are pushed further down to cfw_get_shipping_total() and instead we only check that we have shipping enabled and that the cart has items.