It seems to me that the only "compromise" that could be reached here is for Goodell to appoint someone like a Judge (as he did with Rice) to hear Brady's appeal of his penalty. The players labor agreement with the NFL provides that the commissioner or someone he appoints is to hear the appeal so that is not anything that will be heard in a court. If Goodell heard the appeal Brady might then be able to argue that he was biased and had a conflict of interest given the Wells report was put together by the league. That argument would have to be made with an appeal to the NLRB - not a court. By appointing an outside party as the arbitrator, (and particularly if the two sides agree on the appointment), the NFL could avoid that potential argument.
As for the Patriots, they can also appeal but Goodell is the decision maker there. If that appeal is denied, I suspect that the Patriots could appeal to the competition committee (NFL owners), but I do not believe that has been done before.
Brady can file a lawsuit against the NFL for something like defamation, but that should not affect the processing of his grievance claim.
