At the risk of oversimplification, the core issue was simply whether, under the CBA, Goodell had to abide by any notions of due process or, in the name of expediency, "anything goes" up to and including defamation and "facts" spun from whole cloth. For whatever reason, 2 judges felt the later was the correct call. It's totally speculative whether another lawyer could have reasoned them out of such an absurd interpretation of "deference to the arbitrator."
You typically can't reason someone out of a position they didn't reason themselves into no matter how good you are or how big a reputation you have.