Line a rimmed baking sheet with parchment. Arrange bananas, 3/4 cup strawberries, the mango, sweet potato, and pineapple on pan in separate bands and freeze, covered, until firm, about 2 hours. Set 2 large, wide glasses (about 18 oz. each) in freezer to chill.
Make strawberry layer: Moisten thin strawberry slices with water and attach to inside of chilled glasses around bottom; set in freezer. In a blender, whirl 1/2 cup yogurt, the bananas, frozen strawberries, a generous 1 tbsp. honey, the lemon zest, and lemon juice until smooth, scraping inside of blender as needed. Spoon mixture into glasses and set in freezer. Rinse blender.
Make mango layer: In blender, whirl 1/2 cup yogurt, the frozen mango and sweet potato, a generous 1 tbsp. honey, the lime zest, and lime juice until smooth. Gently spoon mango mixture around inside edge of each glass to create a clean horizontal line. Return glasses to freezer. Rinse blender.
Make pineapple layer: In blender, whirl remaining 1/2 cup yogurt, the frozen pineapple, remaining generous 1 tbsp. honey, 3 tbsp. coconut, and ginger until smooth. Carefully spoon onto mango layer as before. Set 2 tbsp. remaining coconut on top of each smoothie.
* Microwave a whole sweet potato until tender, 6 to 8 minutes.