Tracking the Rift's position and orientation about a fixed origin (relative to the camera)

I'm working on a project (in Unity 5) which requires absolute position and orientation tracking relative to the camera. This is in combination with Leap VR hand tracking and some physical equipment (fixed relative to the camera) which the user interacts with while in VR. The runtime clearly knows the information I need - is there any way of extracting the transformation from camera-tracking space to the tracking space presented by the runtime?

What I've got at the moment is a kind of reverse-calibration which 'corrects' the tracking transformation so that the camera position and orientation is fixed in the scene, but that seems archaic and doesn't work properly when the camera is pitched up or down.