We are seeing a behavior (on every one of these servos that we test) that it won't go between arbitrary angle values. If the angle we want to go to is too far from where the servo is currently positioned, then it either ignores the new target value, or very slowly creeps to it if it's not "too far". If the target angle is "close", say within 15 degrees, the servo will correctly and quickly move to the target angle.
So far, we've looked at voltage (right at the top of the spec for the servo), signal quality (nice solid 50Hz square wave coming from a PCA9685 16-Channel 12-Bit PWM Servo Driver), and software (used a hobby R/C tester).
Any and all suggestions appreciated.