I was in the same situation as @maxicandi, so if it helps, here’s how I solved my problem:
The theme I was using had a checkout template included. By deleting this my-theme/templates/checkout.html file, my checkout page once again used the content I had chosen in /wp-admin/edit.php?post_type=page.
So I put the shortcode [woocommerce_checkout] there, as it takes into account all the “actions” I’d added, especially woocommerce_checkout_billing.
