As we seemed to be going round in circles, I decided the best thing to do was completely uninstall MLM and start over. I backed up to data from the MySQL db, completely wiped everything out and manually re-installed MLM on my server.
I did a quick test of functionality and then re-imported the data back into the database.
All of my history is there and, joy of joys, bounce tracking is now working.
So to complete my task, is there anyway I can resend all the bounces to MLM from the history in EBH? Obviously, all the bounces have been deleted from the mail server, so I can't go back in time. But I would really like to have the tracking information in my stats.