For the cheesecake: Position a rack in the center of the oven and preheat it to 325 degrees F. Lightly spray an 8-inch springform pan with 3-inch-high sides with nonstick cooking spray.
In the bowl of an electric mixer fitted with the whisk attachment, place the egg whites and salt. Beat on medium-high speed to soft peaks, 2 to 3 minutes. With the mixer running, slowly rain in the evaporated cane juice. Increase the mixer speed to high and beat until the egg whites are glossy and hold stiff peaks, about 2 minutes. Sift the flour over the whipped whites and gently fold until smooth. Scrape the meringue into a clean bowl. (And hey, guess what? You just made a small batch of angel food cake batter!)
Into the mixer bowl (no need to clean it), place the cream cheese. Place the bowl back on the mixer and fit the mixer with the paddle attachment. Beat on medium speed until creamy. Add the honey and beat until smooth. Beat in the egg yolks one at a time. Add the lemon juice, vanilla extract and lemon zest and beat to blend well. Reduce the mixer speed to low and stir in the yogurt.
Carefully fold about a third of the egg white mixture into the batter to lighten it. Gently fold in the remaining whites until the batter is smooth. Scrape the batter into the prepared pan.
Bake until the cake is puffed, lightly golden and mostly set but with a slight wobble when the pan is jostled, 45 to 50 minutes (a toothpick won't tell you much about doneness; it's best just to rely on visuals here). Turn off the oven and let the cake continue to cook in the oven for 1 hour. Cover and chill in the refrigerator for at least 3 hours. When ready to serve, unmold the cheesecake and put onto a serving platter.
For the topping: In a medium bowl, whisk together the honey, hot water and vanilla. Add the apricots and blackberries to the bowl and gently toss to coat. Top the cheesecake with the honey and fruit mixture, slice and serve.