Exactly what I needed

I’ve been looking for something like this for a long time, and was using a finicky home-grown solution.

Works as expected!

Hidden feature (thanks @uamv):

Set defaults in your theme with

function PREFIX_set_default_glances( $glances, $user_id ) {
  unset( $glances['post'] );
  unset( $glances['comment'] );
  $glances['products'] = array( 'icon' => 'f174', 'sorted' => 5 );
  $glances['solutions'] = array( 'icon' => 'f507', 'sorted' => 6 );
  $glances['markets'] = array( 'icon' => 'f238', 'sorted' => 7 );
  $glances['press-releases'] = array( 'icon' => 'f157', 'sorted' => 8 );
  return $glances;
}
add_filter( 'gt_default_glances', 'PREFIX_set_default_glances', 10, 2 );