I am one of those who absolutely hate the customizer, I shouldn't say "hate" but that describes just how much I dislike it and how much I have been saddened by all the human effort that has been poured into it rather than other parts of the WordPress project. But WOW, that customize-direct-manipulation plugin (maybe it needs a better name) changes everything. Now, thanks to it the customizer finally makes sense.

Concerning the theme compatibility issues, and more specifically the z-index and color cases, maybe the plugin could add some settings page to the backend where the user (or more maybe even the theme author) could set their appropriate values and styling.

Anyway, thanks for fixing the customizer experience.