After much planning and experimentation, we realized that we don't really need to use a green-screen for the head removal. As the motion is only along one axis, and the camera is fixed for this shot, we can remove the head in post-production using a simple mask.
For this test, we used ping-pong balls as motion trackers for the head and the broom. We shot the head without any green screen or mask. I had my head turned up so that my head wasn't casting any shadows on the neck and chest. We also shot a footage of just the background wall so that we can use it to mask out the head.
For the broom we hand-held a green poster paper behind it and walked it across the wall, so that we would get the exact lighting conditions.
Later using After Effects we tracked the ball in both the shots and composited the broom over the head. We used a simple garbage mask to clear up the noise on the green screen for the broom. After Effects does not support attaching masks to trackers, so we found this script from AExtensions that does that and used it to move the garbage masks.
For the final shoot we plan to use 3-4 trackers so that we can get head motion, rotation and swivel data. We plan to build a tree branch prop that would be used in place of the head.