I believe that the approaches that we designed could be implemented/extended to document-oriented DBMS. Since I don't have any experience with those DBMS, I have no intuition on whether the approaches would uncover any bugs.

Implementation-wise, supporting CouchDB and MongoDB in SQLancer would be feasible. SQLancer shares little infrastructure between the testing implementations for the individual DBMS, and thus imposes only few restrictions on them. We would definitely welcome implementations for any NoSQL DBMS in SQLancer!