I will say this: the folks who keep saying that Goodell should have swept this under the rug are misreading the level of resentment and outright hatred that exists in the NFL community for the Patriots.
People outside of NE look at the Pats the way we looked at the Yankees 10+ years ago. They are seen as an arrogant, entitled organization that bends the rules when it suits them and shows no remorse when caught. It's not right, but the perception is real.
There is no constituency for vacating Brady's suspension, the loss of draft picks, etc. Goodell faces no uprising among the owners for acting recklessly. (Hell, they were rooting him on.) In short, people within the NFL community don't care about the evidence - they believe the accusations. And they want to see the Pats get what's coming to them. They don't fear Goodell turning his ire towards them because they believe that they aren't like the Pats. (Of course, this is not too dissimilar to how Kraft felt about Goodell when he rallied to his side last fall. So there's a karmic justice at work here.)
In short, Brady and the Pats have no play here except to push ahead as aggressively as they can. Brady will win. The team almost certainly will not. But if they feel they have been treated unfairly, they need to push their claims aggressively. Perhaps with a bit more tactical finesse than yesterday.