They DO have a case.
Of course they do not have a case, for the same reasons that many have stated in this thread. As you said, they didn't change the substance of the petition, only cleaned up the form so it doesn't seem so amateur.
It is not Christian-like to me. Nothing Jesus would advocate, and it seems to be a form of extremism.
Yes, it's un-Christian and extreme, but that's not what makes a violation of the law. I would be shocked if a law firm actually is "getting involved" in this in the sense of taking it on as a case. Maybe they will send it on their letterhead to some officials, but I would like to see a press release or something before I believe that they are actually doing anything meaningful.
That is why, the former JW's can make a valid case at the UN
You can't "make a case" at the UN. You can send them a letter, but there is little they can do even if they agree. The document you cited has no teeth. And besides, it's too general to even establish that the WTS violates it. It is primarily directed at governmental intrusions into someone's ability to change their religion. Do you have any authorities, other than personal opinions, that institutional shunning is "coercion" as defined by the UN? And even if it was, isn't their right to nonviolent shunning part of their own right to freedom to worship as they like, according to the same document?
It almost sounded like some of the comments here didn't want anybody to have success in stopping what the society does.
I don't know about others, but personally, although I don't like shunning and authoritarian dogmatic religions, I hate authoritarian government overreach and censorship more, and I know that the latter can be far more dangerous if unchecked.