Steven Zahm@ Joel
Unfortunately it seems their frontend editor overlay seems to take over the core WP Customizer API (or blocks its usage) which is what Connections uses for its Template Customizer. I highly doubt there’s anything I can do about this because this really isn’t “stock” WP. You’ll have to ask Sharefaith support if there is a way to get back to the core WP Customizer rather than using their frontend editor overlay. I do have the feeling since they are a managed WP service there is not going to be a way to do this. I imagine you’re going to run across other such limitations since core WP is slowing moving towards using the Customizer as the definite way to customize a site.
Luckily, much of what can be done using the Template Customizer can also be done with shortcode options. See this section of the cMap doc page:
http://connections-pro.com/documentation/cmap/#Advanced
Hope that helps!