My solution (download TXT file) was to write a bit of PHP code that determines whether the article in question was posted before or after my SSL certificate was installed. Note that this script uses Shareaholic as its example, but you can also adapt it for AddThis or whatever social sharing button service you like. I saw that Shareaholic Pro accounts, and some premium (paid) share-plugin-developers offer solutions to this problem, but I'm not looking for another ongoing expense.
I wound up writing my own code for this because other solutions (here, and here) used Javascript in their implementation and didn't seem as solid as my PHP method. (download TXT file) The way my code works is for non-SSL sharing button code section, it includes the 'data-link' command so that you can override the URL of the page being shared.
In addition to using this code structure for fixing the share counts after adding SSL, you can also use this technique to change domain names, extensions, moving the site into a subdirectory, etc...