Angelpie, the method you describe is my understanding of how Rose came up with the Rose factor. Just by baking each layer multiple times until she hit the right amount. You may just have to keep experimenting, although I wonder if Rose chose a tube pan for this cake because of this issue—not sure.
You basically need the cake to have a stronger structure to keep from dipping. Besides lowering the baking powder (BP weakens the structure), another idea would be to replace some of the yolks with whites, as they provide a stronger structure.