Stephanie Stradley
Though the Goodell is entitled to hear the appeal under the CBA, he may refer it to one of his other inside-the-NFL minions. He likely will resist sending it to an outside the NFL source because he usually loses when that happens.
I believe that the Wells Report is vulnerable if a truly outside source looks at its content. I am guessing Kessler already has the transcript of Wells' remarks as an exhibit, because that defensive presser seemed good for PR points but not so good if you are still in the midst of the discipline process and resolution.
If after appeal, Brady doesn't want to live with the result, the NFLPA may file an application to vacate the result on Brady's behalf.
Theoretically, Brady could go the Saints Jonathan Vilma approach and file a collection of defamation claims. (He had 11 claims for relief in his original claim). Basically, Vilma's lawyers cherry picked all the grandstanding things that were said publicly about him that were untrue, and argued the alternative view in the complaint.
It seems like the discussions of Deflategate have tended to be less inflammatory than Bountygate statements, and I think maybe that is one thing that the NFL has learned from that.
It never got to a final adjudication but did put pressure on the league to reverse course. They certainly didn't want to go too far into discovery.
There are plenty of reasons why a person who believes they were legitimately defamed would not file such a claim. Defamation cases by public figures are hard to win. They are expensive, time consuming, unpredictable, and privacy invading. And I don't even think Tom Brady has enough money to want to get into a civil lawsuit with the NFL, which has enough money they should be a part of the U.S. Treasury.