Position an oven rack in the center and heat the oven to 400°F. Coat a 13×9-inch baking pan lightly with cooking spray, reserve about 1/2 cup of pretzels for garnish, then process the remaining pretzels with 1/4 cup sugar-free sweetener for about 15 pulses. The crumbs should be coarse rather than powdery, with small pieces left for texture.

Add the melted butter to the processor and pulse about 10 times until the crumbs hold together when pressed. Pack the mixture firmly across the bottom of the prepared pan with the base of a measuring cup. A firmly compressed layer bakes into an even base instead of loose crumbs.

Bake the crust for about 10 minutes, turning the pan halfway through the baking time. Let it cool for about 20 minutes after it comes out of the oven. It should smell toasted and look lightly browned at the edges before it begins cooling.

Beat the softened cream cheese with 1/2 cup sugar-free sweetener on medium speed for about 2 minutes, then slowly stream in the heavy cream at medium-high speed. Whip for about 1 minute more, scraping the bowl when needed. Stop when the filling holds soft peaks and looks airy enough to spread without running.

Spread the cream mixture over the cooled crust, pressing it tightly against all four sides and corners of the pan. Refrigerate for about 30 minutes until the dairy layer feels set. Check the perimeter closely so there are no open channels where strawberry liquid can slip underneath.

Blend 2 pounds of thawed strawberries with some of their juices for about 30 seconds, then strain the puree into a medium saucepan through a fine-mesh strainer, pressing with a small ladle. Whisk in the remaining 3/4 cup sugar-free sweetener and salt, then heat over medium-high for about 5 minutes. Remove the pan when the sweetener has dissolved and small bubbles gather around the edges of the puree.

Sprinkle the gelatin over the cold water in a large bowl and leave it for about 5 minutes, then whisk in the warm strawberry puree and stir through the remaining strawberries. Chill the mixture for about 30 minutes until it lightly clings to the bowl, pour it gently over the cream layer, and refrigerate until fully set, at least 4 hours or overnight. The topping should coat the back of a spoon and flow in slow sheets, rather than pouring like thin juice.