Adam - although MS seems to think our issues are not related, I managed to fix mine today...I think.
It was not easy, but basically I uninstalled both Outlook 2011 and 2015 for Mac, including going into the sub-directories and deleting my "identities." Then I reinstalled Outlook 2011 (I assumed this was an Outlook 2015 problem so I haven't reinstalled it).
Outlook 2011 worked fine after reinstall, BUT all the duplicate meetings still appeared on the OWA and my iPhone. Even after I re-synced everything the meetings stayed on OWA and iPhone but never reappeared on the desktop client. BUT they also stopped multiplying.
Then came the hard part...I went into the OWA and deleted them one-by-one. That also deleted them from the phone.
That was 3 hours ago...so far no sign of the original meeting or any multiplying meetings on the desktop, OWA or phone.