I think you're being a bit unrealistic if you expect this to change opinions. Surveys in Saudi Arabia show overwhelming support for beheadings and honour killings and cutting off limbs. They do it in the public square. It's an everyday event. Most the people in Saudi Arabia wouldn't blink an eye at this and there would be widespread support for them. They want strict sharia law. They're not against it; it's widely popular.
And it's sanctioned according to Islam:
A Jew came (T. was brought) to the apostle and said that he had seen Kinana going round a certain ruin every morning early. When the apostle said to Kinana, â??Do you know that if we find you have it I shall kill you?â?? he said Yes. The apostle gave orders that the ruin was to be excavated and some of the treasure was found. When he asked him about the rest he refused to produce it, so the apostle gave orders to al-Zubayr b. al-Awwam, â??Torture him until you extract what he has,â?? so he kindled a fire with flint and steel on his chest until he was nearly dead. Then the apostle delivered him to Muhammad b. Maslama and he struck off his head, in revenge for his brother Mahmud.â?? (Ibn Ishaq 515).
And Mo himself:
Muhammad is depicted in a hadith as saying: â??Certainly I decided to order the Muâ??adh-dhin (call-maker) to pronounce Iqama and order a man to lead the prayer and then take a fire flame to burn all those who had not left their houses so far for the prayer along with their houses.â?? (Bukhari 1.11.626)
What makes you think this would turn opinion against IS?