I believe that I found the source of the issue (or at least masked the symptoms). It looks like the problem happens when Alert Central has not processed any email messages for several hours/days. When this happens, it looks like some processes get cold and out of sync with each-other, causing it to begin processing an email, and then process the same email a second time before the first process completes. I setup a scheduled task that generates an email to Alert Central every 30 min, which I then have a rule on Alert Central to trash the alert email. This seems to keep the processes warm enough that I have not had a repeat of the double-alert issue since I set this up.
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