Part 7:
The reported measurements are as follows:
Angle -10: 102.24
Angle 0: 107.62
Angle 10: 113.86
Angle 20: 120.28
Angle 30: 126.11
Angle 40: 131.53

Part 8:
The top of the object gets pretty close to accurate if I am meticulous
about measurements. However, my calculations do seem not as precise with 
even slight inaccuracies in the reported coordinate. I did not use any
shift in coordinate schemes for the head titlt since I simply needed to
find the absolute angle to set the head tilt. As such, I simply used the
precalculated translations between the head, camera and base.