Hi Mark,
1) I started to do an extension for the Customizer 2 years ago. But the more developing, the more I realized that I had to rewrite the whole plugin to port it to JavaScript. So, I stopped. At the moment, the MB Settings Page only supports back end pages, not in the Customizer.
2) To make it compatible with Customizer, you need to set 'option_name' => "theme_mods_$themeslug"
in your settings page. Then the MB Settings Page will save data into theme mods, which are used by the Customizer.