Using empties (nulls) to orientate a solid in After Effects

I’m trying to overlay some motion graphics I’ve created in After Effects on to an image sequence rendered from Blender.

I’ve create four empties on the corners of my object in Blender and used the Blend2AE script to export my camera and empties from Blender. In After effects these all line up perfectly with the rendered sequence.

I now want to create a solid (my mograph precomp in reality) that will align to the face of the object using the empties (now nulls in AE). Is there an easy way to do this? Corner pinning doesn’t work because the empties don’t actually move, it’s the camera that moves, so there’s no position data actually changing. I can make the layer a 3D layer and copy the position of one of the nulls to the 3D layer, but it’s only ever forward facing.

Does anyone know how I can line this up? Much like the camera tracker in AE will let you create a solid from several tracks and it will be properly aligned.

I could track it in Mocha and use that corner pin but that sounds like rubbish to me since I already have the camera and null positions.