YAY!
When the company pushes packages to desktops / laptops, they create a folder in which the upgrade files are kept. This allows uninstalls, fixes, etc. without having to repush stuff. I found the 100\DTS\Binn folder in one of those, copied it over to the official Program Files path, reopened the package in Data Tools and no COM object error!
Whoo hoo!
Thanks for your help, guys. I appreciate it.