Prepare the simple syrup by combining the monkfruit sweetener and water in a small skillet. Stir to combine and heat until the sweetener dissolves completely, approximately 3-4 minutes. Remove from heat and set aside to cool.
Place the strawberries, lime juice, rum, and one-quarter cup simple syrup into a blender and blend until smooth.
While the blender is still running, add the ice a little at a time until thoroughly combined. Turn blender off and remove lid. Taste and add additional simple syrup, if desired, and blend for another 30 seconds to combine.
To serve, pour into glasses and serve immediately garnished with lime wheels and/or whole strawberries.