The only way to get out of this for Goodell is to hold all penalties in abeyance, and do a league wide longitudinal study of all footballs in the 2015 season.. the science is nice, it cannot replicate game and atmospheric conditions.. postpone everything until this study is completed.. both parties would have to agree upon who does the study as well.
There can be rumors of some sort of negotiations, but anything more than a small fine is completely unacceptable..
Of course, Goodell can allow it to go to Federal Court and then it is out of his hands, but that will not escape the scrutiny of the owners who will look at Goodell with a "crooked eye" regarding the money spent and lack of "common sense" decision making... it would be sad for the commish to blame the Court.
Brady going to Court could have long term implications for the NFL, particularly as it relates to standard of evidence, due process and conflict of interest.. the NFL also does not want "discovery" to show their inner workings... The NFLPA and Brady have "deep pockets" and could depose everyone in the NFL offices who had any knowledge of their corrupt practices..