There were plenty of results on a Google search for the key phrase, but none of them provided a solution (plenty of them blamed everything but Outlook, though). Fortunately, I found a workaround which seems to work for now, but it relies on still having the original meeting request messages available and an external IMAP client (so obviously you need to be able to talk to Exchange via IMAP).
Basically, I just deleted the meetings from my calendar, and then found the original request messages. They still showed me as being the organizer with the added wrinkle that the items were "no longer on the calendar," BUT if I used a different email client (i.e. Thunderbird over IMAP) and moved the items back into my inbox, then Outlook finally saw them as they originally were, and I was able to accept the meetings appropriately.
It's fortunate that both of these long-term recurring meetings happened to have been originated recently, though. If I didn't still have the original meeting request emails, I'd have been out of luck.