I know you are busy so I appreciate you looking at this.
I am a big fan on your script, however after 3.7.1 (I am not 100% sure it was after the update, but we didn't notice it until after the update) when we go to to the Theme Customizer page it is blank on the right (though the customization options are still there).
I have experienced this before and forcing the DM setting "Redirect administration pages to site's original domain" fixed the issue. However it doesn't seem to do the trick any more.
If I go to a site that does not have a mapped domain, the theme customizer works without issue. If I load a site that has a mapped domain, even though the URL is showing the original subdomain, the live preview portion of the theme customizer is blank.
Any tips would be greatly appreciated. I will be happy to provide you with any information I can.