Preheat oven to 350°F. Whisk together flours, baking soda, and salt in a large bowl.
Beat butter in a large bowl with a mixer until light and fluffy. Add sugar; beat until well combined. Add eggs, 1 at a time, beating well after each. Add vanilla; beat until just combined.
Slowly add flour mixture, and beat until well combined. Add oats, almonds, seeds, coconut, raisins or currants, mango, and papaya, and beat to combine.
Form dough into 8 cookies (using 1 cup each) or about 14 smaller cookies (using ½ cup each), and place on 2 parchment-lined baking sheets. Top each cookie with 3 banana chips.
Bake until golden and firm, 30 minutes for large cookies and 20-25 minutes for smaller cookies. Let cool completely on baking sheets, about 30 minutes.
