If anyone finds this having the same/similar errors, the solution was simple:
chown :nginx -R /var/lib/php/ (the apache group previously owned it and I am using nginx+phpfpm with the ADFS plugin)
I identified it as the issue by placing "dbglog(Is this repeating?)" within the "dokuwiki/lib/plugins/adfs/auth.php" if block that checks to see if SAMLResponse was set. With debugging enabled, I noticed that the message did in fact repeat the 6 times in the log. From there, now knowing it was a session/cookie issue, I was able to identify that sessions weren't being tracked.
"ADFS: The status code of the Response was not Success, was Responder" Is not a very detailed error and certainly didn't mean anything to me. But for anyone else that sees that, check your ability to track sessions. 🙂