Theme Customizer – Choose where widget area appears, to let users organise widgets

You can move around sections in the customizer simply by accessing the datastructure and assign a different value to the panel. So supposing that your widget area, created in the usual way, is called wpse210938_area and you want to move it to the panel wpse210938_panel, you do this:

add_action( 'customize_register', 'wpse210938_move_widget_area' );
function wpse210938_move_widget_area () {
  global $wp_customize;
  $wp_customize->get_section ('sidebar-widgets-wpse210938_area')->panel="wpse210938_panel";
  }

Only disadvantage is that, if you have debug mode on, you will get a php warning “Creating default object from empty value”, presumably because WP loads the widget sections last, so when you are moving them, they are still empty.