Is there a way to use a token in the redirect?

I think the best way to accomplish this is to write a small custom module that handles the static path and redirects to the logged in users page or some other page if an anonymous user.

This is pseudocode but you'd want something like this:

foo.module

function foo_menu() {
  $items['path/to/your/static/url'] = array(
    'title' => 'static url redirect',
    'page callback' => 'foo_static_url_redirect',
    'access callback' => TRUE,
    'type' => MENU_CALLBACK,
  );

  return $items;
}

function foo_static_url_redirect() {
  global $user;

  if ($user->uid > 0) {
    drupal_goto('user/' . $user->uid . '/downloads');
  }
  else {
    drupal_access_denied();
  }
}

I posted another solution, using hook_redirect_alter to apply user tokens, here: http://drupal.org/node/1331582#comment-6092790

Let's close this as a duplicate of #1331582: Use tokens for redirects then