Have a look at https://fetchify.com/
We used fetchify really successfully for almost 3 years providing exactly the functionality you require. Customers loved it, until Shopify stopped the method used for injecting code on the checkout page on standard stores. Rather than solve the user need, they just blocked it.
Unless you are using shopify pro you cannot modify the checkout pages - therefore cannot achieve what you want to do.
A cynic may suggest Shopify identified a loophole and a way to force merchants to upgrade to Pro to get this functionality.
I've asked support several times and waited for the new fetchify app, but it looks like this is just another postcode validator.
If you find a solution please share.