Now I know why the NodeBB integration broke.
Short version: the official method to export and import involves dumping to a JSON file. Despite exporting the unique ID numbers of each post, when they are imported, it generates a new set of unique ID numbers - which do not match up with the entries on the NodeBB side.
I believe the next time I do this, instead of importing a JSON file, I should follow the backup / restore procedure I'd already tested, namely, replace the database. The ID / verification numbers in the JSON file are also stored in the SQLdump, and flat out doing a replacement import of the DB will ensure all of the post ID numbers stay the same.