[Maya to Unity] Baking a blend-shape animation to FBX

I have an animation of a plane being deformed by blend shape consisting of 4 in-between target meshes.

Looks great in Maya, but I can't figure out how to bake the topology of my plane into an FBX. Is that even possible with multiple blend targets? Note: I don't need to adjust the blend envelope in Unity, just play a baked animation.

I've tried everything I can think of. My only other thought was to export the mesh at each frame of the animation (only 32 frames) and cycle through them with a script, but I'd obviously want to try that only as a last resort.

Thanks for reading.