Hi KeithLwood,
Thank you for the detail issue description.
May I first confirm with you if you are using Gmail account at outlook client or you are using Office365 account with its mailbox, it will be great if you tell us your account type.
Since you have already did almost all the troubleshooting steps, regarding with the clean up boxes, can I ask if you did this as well?
Open Outlook > File > Options > Mail > Under Conversation Clean up, Uncheck When a reply modifies a message, don't move the original > Restart Outlook (it is is already unchecked, check it Restart Outlook, Uncheck it and Restart Outlook)
Also, try to Account Settings > Open your account > More settings > Under Advanced tab, put INBOX in Root Folder Path. (If your all folders disappear, simply remove INBOX from here)
Last, we would like you to create a new profile, navigate to control panel, Mail, and create a new one for your convience:

Let me know if the above steps work to some extent, apprecaite it.
Kind Regards,
George