In your case you can edit the following code to accomplish what you are looking for by assigning the custom taxonomy meta box to a custom context and then running do_meta_boxes
/**
* insert meta boxes before main editor below title
*/
function wpse_140900_add_meta_boxes_after_title( $post ){
// per the comment below filter by post type
// http://wordpress.stackexchange.com/questions/140900/how-do-i-make-a-custom-taxonomy-for-a-cpt-appear-inbetween-title-and-editor-boxe/140906#comment201984_140906
if( $post->post_type != 'targeted-post-type' )
return;
// setup function vars
global $wp_meta_boxes;
$current_screen = get_current_screen();
$registered_taxonomy = 'custom_taxonomy';
// move meta box to after_title position
$wp_meta_boxes[$current_screen->id]['after_title']['core'][ $registered_taxonomy . 'div'] = $wp_meta_boxes[$current_screen->id]['side']['core'][ $registered_taxonomy . 'div' ];
// display registered meta boxes for after_title
do_meta_boxes( get_current_screen(), 'after_title', $post );
// remove meta box from displaying in the "default"
unset( $wp_meta_boxes[$current_screen->id]['side']['core'][ $registered_taxonomy . 'div' ] );
}
// init meta boxes after title
add_action( 'edit_form_after_title', 'wpse_140900_add_meta_boxes_after_title' );
In this particular code snippet it will move your sidebar meta boxes below the title and above the content editor fields.