Thanks for the suggestion. You're right that extending the returned JSON in that way would be a more general solution. However, it does add further complication to what's already a rather complicated interface. The Show Differences button should still be displayed to the teacher with the current interface (assuming the showdifferences attribute is set). However it won't actually work if the teacher's language is different from the student's because the specified column headers won't be present. But does that really matter? I don't recall ever using the Show Differences button when reviewing student's submissions.
If you really do want to use it, logging in as the student (using the Log in as...) function in Moodle is probably the best way. That way you see exactly what the student sees, not some partially translated version.