Ampulla of Vater
Illuminator
Personally speaking, I don't give a damn about "winning hearts and minds". I am not an advocate. I am not even a "supporter" in an active sense of the word. I am someone who finds this subject interesting and who has some opinions on it. I appreciate a forum in which I can debate those opinions, have them challenged, challenge others' opinions, and generally become more well-educated and enlightened about the case.
Aside from my personal motivation, I'd also ask why anyone - even true advocates and partisans - should be overly concerned about any "battle" for hearts and minds, and in particular the hearts and minds of the general public in whatever country. There might be some limited value in trying to convince the genuine decision-makers (courts, politicians etc). But I don't think that this forum (or anywhere else on the internet, for that matter) would be a particularly good means of attempting this. Rather, a forum such as this might be useful in terms of generating ideas/strategies, and "road-testing" them, prior to any approach directly to decision-makers.
As regards the general public, though, I would imagine that the only people who worry about what the general public think would be Knox and Sollecito themselves, and their families and close friends. And they have a far, far better chance of communicating with the general public via either the mass media or their own social networking/blog sites, rather than a rather specialised forum such as this. And in this regard, it would appear that Knox in particular has had a significant degree of success in "winning hearts and minds" of the public in the country which (presumably) matters most to her: her home country of the USA.
I would think it matters what Mr. and Mrs. Average think when it comes (if it comes) to extradition. I imagine a huge groundswell against extradition would be what a citizen would want. But you are correct, they can probably get that going themselves, via social networking.