Just to be clear: -

'Control panel / Programs and Features' list does show Office 2007 as being installed and you can select it and choose it before selecting 'Uninstall / Change' but this "does nothing". Is this correct?

Office 2007 was working okay before 'migrating' to Office 365? Is this correct?

What do you mean by 'migrated'? Did you leave 2007 installed and simply subscribe to Office 365? If so I wonder if Office 365 has affected Office 2007 by becoming tied-into it somehow?

Maybe some expert will be able to help you. I only ask these questions before some expert does in order to clarify things for them first.