You probably won't be able to get them reliably directly. But if you check all comments live, it is possible. In SDS, the comments also contain the root permlink (I don't know whether this is also the case with the Steem API).

The Steem API has the root author and permlink, too. That's how I was thinking to get it. It would be nice if I could find a way to avoid that second query, but (without secondary storage), I don't think there's a reliable way. As you noted.