You can include the same file in template-composers-terms.php
and template-interprets-terms.php
like that :
<?php
/* Template Name: List of composers */
$tax = "composer";
require "include/file_which_does_all_the_work.php";
and if the page slug is the same that the taxonomy slug, you can save the line $tax = ...
with that in the included file :
$tax = $GLOBALS["wp_query"]->query["pagename"];