How to modify admin headers

Question

Not a direct answer, but: for simple data exports on the admin side, I generally just use the AJAX API. Set up an AJAX handler for your export:

/**
* export from admin
*/
function wpse_126508_export() {
    header('Content-Type: text/xml; charset=utf-8');
    header('Content-Description: File Transfer');
    header('Content-Disposition: attachment; filename=wpse_126508_export.xml');

    $xml = new XMLWriter();
    $xml->openURI('php://output');

    $xml->startDocument('1.0', 'UTF-8');
    $xml->startElement('wpse_126508_export');

    // ... your details

    $xml->endElement();     // wpse_126508_export

    $xml->flush();

    exit();
}

add_action('wp_ajax_wpse_126508_export', 'wpse_126508_export');
add_action('wp_ajax_nopriv_wpse_126508_export', 'wpse_126508_export');

Then output a link to it on your admin page:

$exportURL = add_query_arg(array(
    'action' => 'wpse_126508_export',
    'nc' => time(),     // cache buster
), admin_url('admin-ajax.php'));
printf('<a href="https://wordpress.stackexchange.com/questions/126508/%s">export</a>', $exportURL);

Of course, you can equally submit a form to the AJAX endpoint if you need to post your request.