Typically, what is the function between pulse width and angle in a servo motor?
I would expect much closer to 1500 for center, but that's off-topic.

A hobby servo, with the main intent being to be placed in a closed-loop control system (where the driver, a human, closes the loop) is not required to behave precisely. Add on to this that the control link itself may be non-linear, and the output of the system may also be non-linear (doubling the throw on an elevator does not necessarily exactly double the rate of rotation of the aircraft). The human won't even notice non-linearity. In fact often we add curves (expo) to the system for more precise control around center stick, and more aggressive throws at the extents.

That being said, I would expect Futaba, if anyone, to make relatively predictable servos. The control loop may in fact be linear, but the feedback within the servo may not; a servo uses a potentiometer for position feedback, potentiometers are tricky and often imperfect. 

A hall sensor, brushless servo will be more accurate, assuming that it's trying to be linear. A separate, more predictable position feedback (a hall sensor potentiometer) may also work. The ideal solution here is a stepper motor, where precise angular displacement is predictable, as that is the intent of the design.