I installed the Customizer in a new WP 3.7.1, running with a WooCanvas 5.5.3-child theme & WooCommerce 2.0.19. And I'm sorry to say: I doesn't work out.
My best guess is that it somehow interferes with the "Email Inquiry"-plugin (http://wordpress.org/plugins/woocommerce-email-inquiry-cart-options/), which also changes the product buttons. But I just want it to change the shop grid layout, and it doesn't show.
Sorry, I know this is not much information, but any ideas?
PS: the other plugins I use are the standard WooCommerce extensions (WooDojo and WooSidebars) and the Yoost SEO.