C4D Animation Import difficulties

EDIT: Added screenshot

I wasn't able to find a similar question to this: I have a C4D project that has a 2.5D animated character in it and I'm trying to figure out how to correctly import it.

The unusual part about it is that instead of being one model animated by bone deformation it is a series of different meshes that make up different frames of the animation. (Think of it like a paper flipbook, each frame has its own mesh (2D plane) and inside of C4D each mesh is only enabled in during the frames it should be shown with layer visibility and keyframes.)

I've imported both the .C4D and an exported .FBX, but in both cases every mesh is always visible. Is there a way to configure either C4D's export settings or Unity's import settings to use the layer visibility information?