Hi, Aaron.
It's hard to draw any conclusion as picture we have is still quite fragmented. Can I ask you to create a capture of the whole this "looped sequence" from your browser perspective? Some tools that could be easily used for this:
1. [FiddlerCap](http://www.telerik.com/fiddler/fiddlercap) (Windows-only)
2. You also may try installing Firebug addon for the Firefox, and use method described [here](https://knowledge.kaltura.com/faq/how-capture-network-traffic-logs-kaltura-support#firebug) (or may be some other method mentioned on the page will suite you)
3. As a last resort you could use "SAML tracer" Firefox addon, it allows to export all captured HTTP packets, but it's not very convenient.
4. If you are already familiar with this kind of tools, Burp or ZAP or Fiddler proxies may be the best choice for you.
Currently, judging by Apache's log, it seems that browser is being redirected from the Google's SP with a SAML request, then (probably) redirected back to it with a correct SAML response, then again is sent from Google to Gluu, and so on.
Please disable any encryption for this TR explicitly (if their SP doesn't require it be enabled, of course), so we could decode SAML messages from the capture.