Thank you for the quick and complete answer, @simon.
An option to show the WP comments form even when there are no comments would be great. The rest should be covered by existing functionality.
@notriddle yes, I am very familiar with the JS embedder. WP-Discourse is superior in so many ways when you can technically use it (self-hosted WP installations only), that it would be a pity to fallback to the JS embedding because of one important detail (the feature requested above).