TrackIR can be set to have a 1:1 movement correlation
Sure.
the underlying driver is actually capable of a full 360 degrees in 6DOF.
The only real limiting factor is that the IR tracking device has a limited field of vision (partially by design).
What about placing the TrackIR overhead and the sensors on top of the google cardboard box and tweaking the settings in the driver? Could that be feasible?
Well that's an easy thing to reproduce on your own.
TrackIR relies on a line-of-sight connection between the imaging sensor (which usually sits on your monitor, but in theory it could be anywhere) and
three spots that emit infrared light back to that sensor, either active ones (infrared LEDs) or passive ones (reflector, in that case the imaging sensor itself emits infrared light).
The TrackIR software explicitely needs all of these three spots to face forward from your head, otherwise the coordinate system would get twisted.
They can be anywhere around your head but they have to "look" forward and hence the imaging sensor has to be in front of your face.
That's basically all.
Now take an opaque ball and place 3 LEDs around it in a way that both suits the above mentioned specification and keeps line-of-sight connection when you look left/behind you/down (e.g. 135 degrees to the left, 45 degrees down)
and with the same arrangement keeps a line-of-sight connection when you look right/behind you/up (e.g. 135 degrees to the right, 45 degrees up).
If that's physically possible I owe you a beer.
Best regards - Mike