Ok, here are the most believable scores I've gotten for Italy yet.
Bergomo: 29% Yamnaya, 58% Anatolia_Neolithic, 10% WHG, 2% CHG/IranNeo, 0.5% Natufian.
Tuscany: 23% Yamnaya, 53% Anatolia_Neolithic, 8% WHG, 7% CHG/IranNeo, 4% Natufian.
South Italy: 13% Yamnaya, 49% Anatolia_Neolithic, 7% WHG, 17% CHG/IranNeo, 15% Natufian.
Keep in mind this is what potential Near Eastern ancestors get....
Anatolia_BA: 56% Anatolia_Neolithic, 34% CHG/IranNeo, 10% Natufian.
Minoan: 78% Anatolia_Neolithic, 18% CHG/Iran Neo, 3% Natufian.
Levant_BA: 25% Anatolia_Neolithic, 18% CHG/Iran Neo, 57% Natufian.
I used David's PCA to get them. When Italians are modelled with WHG, Yamnaya, Anatolia_N, Natufian, CHG/IranN in isolation the scores always get whacky (eg, 20% WHG, 2% Yamnaya). To dodge this problem I modelled Italians with groups who have varying amounts of ancestry from each ancestor: Baalberg_MN, Iceman_MN, Minoan, Anatolia_BA, Levant_BA, and Yamnaya. Next, I got the WHG, Natufian, Anatolia_N, Iran_N/CHG scores for each of those proposed ancestors. Then I multiplied their ancestor's scores to get Anatolia_N, Yamnaya, WHG, Natufian, and Iran_N/CHG scores for Italians.
Maybe, maybe only Southern Italy has significant Levantine influence, hence their similarity to European Jews.