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 ){
    global $wp_meta_boxes;

    // 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;

    // you could create your own context and load meta boxes in context
    // in this case we are moving the side rail meta boxes below 
    // the title and above the content editor
    do_meta_boxes( get_current_screen(), 'side', $post );
    unset( $wp_meta_boxes['post']['side'] );
}

// init meta boxes after title
add_action( 'edit_form_after_title', 'wpse_140900_add_meta_boxes_after_title', 10, 1 );

In this particular code snippet it will move your sidebar meta boxes below the title and above the content editor fields.

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.

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 ){
    global $wp_meta_boxes;

    // you could create your own context and load meta boxes in context
    // in this case we are moving the side rail meta boxes below 
    // the title and above the content editor
    do_meta_boxes( get_current_screen(), 'side', $post );
    unset( $wp_meta_boxes['post']['side'] );
}

// init meta boxes after title
add_action( 'edit_form_after_title', 'wpse_140900_add_meta_boxes_after_title', 10, 1 );

In this particular code snippet it will move your sidebar meta boxes below the title and above the content editor fields.

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 ){
    global $wp_meta_boxes;

    // 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;

    // you could create your own context and load meta boxes in context
    // in this case we are moving the side rail meta boxes below 
    // the title and above the content editor
    do_meta_boxes( get_current_screen(), 'side', $post );
    unset( $wp_meta_boxes['post']['side'] );
}

// init meta boxes after title
add_action( 'edit_form_after_title', 'wpse_140900_add_meta_boxes_after_title', 10, 1 );

In this particular code snippet it will move your sidebar meta boxes below the title and above the content editor fields.