Re-using single CPT code with get_template_part?

You don’t reuse a specific page’s data via get_template_part, you query for a specific page’s data and use get_template_part to output the result. Look at how any of the core-bundled themes use get_template_part within the loop to output the main query for an example.

Query for the page:

$query = new WP_Query( array(
    'post_type' => 'menu',
    'name' => 'monday'
) );
if( $query->have_posts() ){
    $query->the_post();
    get_template_part( 'menus' );
    wp_reset_postdata();
}

Then menus.php outputs the result:

<?php
the_title();
the_content();
// etc..