Here was my solution. A bit of a hack. It works because I'm using two different templates. One is for the members, and another is for the guests. The one for the guests utilizes the t3 framework. For the guests template, I found the head block in the template and I pasted the following under defined('_JEXEC') or die;
<?php
$app = JFactory::getApplication();
$user = JFactory::getUser();
if(!$user->get('guest', 0)){
$app->redirect(JRoute::_("index.php/my-groups"));
}
?>
So far it seems to work pretty well.