Preheat the oven to 350 degrees. In a mixing bowl, combine the cookie crust and the melted butter together. Blend the mixture thoroughly. Press the mixture evenly and firmly on the bottom and sides of a 1/2 sheet pan. Place the pan in the oven and bake for about 10 minutes. Remove from the oven and cool. In a mixing bowl, whisk 4 eggs, brown sugar, cane syrup salt, cinnamon, nutmeg, and ginger together. Add 1 1/2 cups of the cream and 1 teaspoon vanilla to the mixture and mix well. In a small mixing bowl, mash the squash with 1/2 cup of the cream. Mash the mixture until smooth. Whisk the squash mixture into the egg mixture and blend until smooth. Fold in the chocolate pieces. In another mixing bowl, whisk the cream cheese until smooth. Add the remaining eggs, cream, vanilla, sugar and lemon juice. Whisk until smooth. Pour the squash mixture over the prepared crust. In a steady stream, pour the cream cheese mixture all over the squash mixture. Drag a knife from one side of the pan to the other a couple of times to incorporate the two mixtures together. Place the pan in the oven and bake for about 30 to 35 minutes or until the center is set. Remove the pan from the oven and cool completely. Slice into 2-inch bars.