How do I set wp_mail arguments/manually force wp_mail sending based on the sender’s email address?

Perhpaps wp_mailwould be a suitable filter for this case as it is the first one to fire in wp_mail(). So perhaps something as simple as this might work,

// For reference:
// $atts = array(
//   'to' => string, 
//   'subject' => string, 
//   'message' => string, 
//   'headers' => string or array (I think), 
//   'attachments' => array,
// );
function filter_wp_mail( $atts ) {
  if ( false === strpos( '@domain.com', $atts['to'] ) ) {
    $atts['headers'] .= "Postmark: not valid email\n";
  }
  return $atts;
}
add_filter( 'wp_mail', 'filter_wp_mail' );