maybe split the batter in half - the unberried half in first, then the berried half for the 'muffin stump'
I liquefy the bananas so that should help the moisture level slightly
Dairy-free, kid-friendly baking???
Is this child allergic to the whites or the yolks? Most egg allergies relate to the whites, i.e. the protein, don't they? If that's the case, perhaps this child can have baked goods containing yolks.