They did just sue and sue until someone heard them. A large coalition of groups similarly affected were actively changing society. The fear of left wing parties died down after the war. A large chunk of American history, thought, and letters was involved. The Witnesses did not operate in a vacuum. In fact, other groups could have been involved in these cases. I have a strong feeling that the ACLU had a litigation masterplan that the Witnesses fit. The Witnessses must have driven the ACLU lawyers crazy.
Similar to Nixon's enemies list or Hoover's special targets, there is a honor roll of true Americans persecuted during these years. I also suspect that law professors wrote special law review articles so the Court would be influenced in favor of the Witness' liberty.
Different legal issues face the Witnesses now. They are Goliath now. The law is not so clear. It is not motivation for law school profs to write articles. Besides, the justices have signaled how little they think of law review articles now.