If I were the Judge in this case, I'd temporarily set aside the arbitration award as it did not follow federal law because, a) the arbiter was not independent, b) the investigator who derived his authority from the arbiter was not independent and c) the NFLPA was not afforded due process in several areas which I don't want to list here. I'd say, any of these problems would alone be enough to set aside the arbitration.
Then, at the expense of the NFL, I'd appoint an independent investigator AND a new neutral arbiter to start the process over looking at both the NFL and the Patriots and Brady. Everyone now would be under penalty of perjury in a Federal Court and also face contempt charges for not compliance.
I'd then give the NFL the option to drop the case and get the temporary part of the order changed to permanent or if they really think Brady and the Patriots are guilty, let them pursue it to the end with due process. It seems like if each side believes they are right, that should suit both parties. Then they don't have to clog up the appellate courts, I don't risk getting my ruling overturned and we can get back to hearing important cases.
If the NFL drops it, and I were Brady and innocent, I'd sue the NFL and all those involved for defamation. Would I win? More likely than not, no. But I'd try to get all the dirt out of the NFL and Goodell and put them through what they put me through. If Pash took out all the innocent stuff from the Wells report then published it, I'm not sure that isn't a winning case.