Line a 9-by-5-inch loaf pan with plastic wrap, leaving at least a 2-inch overhang on all sides. Peel 2 of the peaches with a sharp paring knife or vegetable peeler (a serrated peeler works great). Cut each peach in half and remove the pit. Slice into 1/4-inch thick wedges and set aside.
Combine the yogurt, cream, 3 tablespoons of the sugar, vanilla and a pinch of salt in a large bowl and beat with an electric mixer until thick, about 2 minutes.
Combine 1/2 cup of the raspberries and the remaining 2 teaspoons sugar in a small bowl. Mash together with a fork until the berries form a thick sauce. Lightly stir the raspberry sauce into the yogurt cream.
Spread 1 cup of the yogurt cream in the bottom of the prepared loaf pan. Place a double layer of graham crackers on top; break some of the crackers into smaller pieces to cover any gaps. Next, arrange all the peach slices on top in a single layer. Top with another cup of yogurt cream, a double layer of graham crackers, and 1 cup of raspberries. Cover the raspberries with the remaining yogurt cream, followed by a single layer of graham crackers.
Cover the loaf pan with plastic wrap and refrigerate for at least 6 hours and up to 12 hours to allow the crackers to soften and the yogurt cream to set.
When ready to serve, unwrap the plastic wrap and invert the loaf pan onto a platter. Remove the pan and the plastic wrap. Peel, pit and slice the remaining peach. Decorate the top of the cake with the peach slices and the remaining 1/2 cup raspberries. Cut into slices with a serrated knife.
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