Just to wrap up for those who are following this or those who may find this post in the future...
The only reasonable workaround that I have found (with lots of help from Nobbir) for this issue is to effectively create two different 'modes' for my GUI. I created a button to toggle between the two modes. When the button is pressed certain controls are enabled while others are disabled. The enabled states are reversed each time the button is pressed. By doing this, I made it impossible for my conflicting controls to be enabled at the same time. Keep in mind that you need to set the enabled states appropriately on startup. Additionally, I added some code to the execution of some of my addin controls so that the 'mode' will change automatically when that is likely to be the desired action for the user. But having the toggle button ensures that the user can switch modes at any time.
This solution is less than ideal, but it is not terrible. It is adequate for the immediate needs of my particular project. In future development, I would like to see much better programmatic access to activate/deactivate and enable/disable states of addin contols.