In Magento 2 checkout page when customer chooses country the page makes an ajax call and refreshes shipping-methods section. Unfortunately I have not found any tutorials how to duplicate what is happening. I suggest Magento 2 should make a tutorial how it is done so developers can duplicate that process. - add custom filters to shipping-methods or payment.
I have asked about that in Magento.stackexchange.com but like normally the checkout page seems to be the most mysterious part of the Magento 2 (no replies).