Spread 3 Tbsp. syrup over bottom of crust. Top with half the banana slices. In large bowl, whisk pudding mixes with half-and-half, yogurt and vanilla until thick and smooth. Fold in 2 cups whipped topping.
Spoon half of mix over bananas in crust. Top with remaining bananas. Spread with remaining pudding mix.
Refrigerate until set, about 2 hrs. Top pie with remaining whipped topping, drizzle with remaining syrup.