I live in sweden and when we need to moist your cake layers here we use like milk and vanilla sugar (whipped together) to brush on each leyer.
But if you bake the your self you would not need to make it moist. You can use whipped cream fillings that contain agar agar or gelatine (to make it stable). And i would never bake one layer at the time, I always bake my sponge cake high and cut out my layers.
If you are afraid it will dry, use fresh/thawed berries or so in the filling but let the thawed dry out some on a paper towel. And let the berries rest between two thin layers of filling.
When I cover a cake before the sugarpaste or what ever, i use a buttercrem with added berries (like 1/2 cupraspberries in a normal recipie)