Hi Derek,
Unfortunately the "Link Out" type of response takes a simple URL which basically gets turned into an HTML page with the javascript function on the frontend: <script type="text/javascript">window.location="URL_GOES_HERE";</script>
The Raw HTML output will allow you to create your own self-submitting form and do a POST. There is no way to cause a browser to pass headers on a redirect, regardless of the method. You will want to use cookies or other means of authenticating when performing an SSO.