The best way to automate the migration of content will be Tabmigrate (as you may have seen in that post). It will output an excel spreadsheet of the content it cannot move over with helpful indications of what might throw the errors. It could be a change in user names, embedded datasource, etc. and you will have to troubleshoot through those individually. Sometimes you might have to publish some workbooks manually. It should not cause any issues with Tableau Bridge.
Let me know if this helps.