We have a hardworking team of professionals in different areas that can provide you with guaranteed solutions to a blend of your problems. Techyv is one of the leading solution providers covering different aspects of Computers and Information Technology. I have troubleshot various Outlook 2016 on MAC connecting to Exchange 2016/Office365 Exchange and the only pattern to the problem is that they started after the latest OS update. Sometimes this solve the problem with Exchange sending/receiving/sync issues. Try deleting the Exchange account from Outlook and recreate it. Possibly removing the account and re-adding it in Outlook could be the quick fix to it (although they would lose their saved autocompletion which a lot of people complain when they lose it).

From a few different places it looks like it could be something stuck in Drafts too (although you said you checked there). I would verify that their Exchange account is the only account within outlook.