The wider public doesn't really care about much for an extended period of time. It seems like, at least with American media, we jump from one scandal to another. I think the only real way that the wider public is going to care is if there is some large salacious scandal that the media can talk about for ratings. If, for example, there is an egregious lawsuit that has all the right elements to get blasted on the news.
I've thought long and hard about this topic, and from the perspective of JW activism I think we need to be focused on how the public views witnesses and from their perspective the only time they interact are those sleepy Saturday mornings every six months. I think the biggest thing, then, that activists could promote is that the person knocking on your door could be a child preditor and you would never know. The witnesses could be sending unreported sick pedophiles to the doors of the public when often the parents aren't home and a small child opens the door. I think that is the biggest lever to push in my opinion