It’s incredible that Shopify still don’t offer the ability to re-order the shipping rates… seems such a simple thing! I’m using a different workaround ( which I don’t think has been mentioned ) which also isn’t ideal but works for me and might for others in certain cases… essentially I add ( or create ) a variant of each product called “Delivery” and set it as “Courier” or “Collection from ” Since variants CAN be ordered how you like, the default is just set to Courier. This also gets around the various issues with Shopify’s local pickup option ( not being able to use PayPal etc etc ) because you select delivery at the add to cart stage rather than later, and you just add those variants to the appropriate shipping policy ( which is free. )
It’s a pain having to duplicate all products you want to make collectable like this, but not too bad, and a programmer could probably create them automatically using the API ( not looked into that because we only have a few such products. )