In a large bowl, whisk together the sour cream, 3/4 cup of the whipping cream, sweetener, and vanilla extract until well combined.
In a blender or food processor, puree the strawberries until smooth. Add 1/2 cup of the sour cream mixture and blend until well combined.
Transfer another 1/2 cup of the sour cream mixture into another bowl and whisk in the cocoa powder until smooth. It will be quite thick so add the additional whipping cream 1 tablespoon at a time until it has thinned out and is of a "spoonable" consistency.
Transfer the chocolate mixture to a frosting piping bag or a large ziplock bag and cut of the very tip. Use the bag to pipe an even layer into the popsicle molds, filling each about 1/3 full. Try to make the layer as even as you can and not get any drips down the sides (as they will show up on your other layers). Use a q-tip to clean up the sides of the mold if necessary.
Layer the remaining vanilla mixture over the chocolate, filling to about the 2/3 mark on each popsicle mold (you can put this in a bag as well, or simply pour it from a measuring cup). Clean up the sides a bit.
Pour the strawberry over the vanilla mixture, filling to almost the top of each mold (again, in a piping bag or from a measuring cup). Insert wooden sticks 2/3 of the way into each popsicles and freeze until firm, about 4 to 5 hours.
To release, run hot water over the molds and gently tug at the stick.