What is a 'hand flown shot'?
"hand flown" shot is just one that is not automated and you are at control on the sticks/dials. Not a term I invented, but from several customers I've worked for when they want to distinguish between automated flights with, for example, DroneDeploy or Pix4D, and "hand flown" shots where you are using the sticks for full control or even using an Intelligent Flight Mode if you wish, like Tripod or Course Lock, where you are in control with the sticks but the stick output is moderated by some other function.
I think you should look at the EXP settings that determine the sensitivity of the yaw stick. I use a setting around 2.8. You need to experiment to find your sweet spot.
Like you suggested, JeffreyS, the Exponential, Gain, and Sensitivity settings were the first things I checked and they are all quite low or moderate:
Rudder Right EXP is negative .10
Sensitivity Attitude 40, Brake 80, Yaw Movement Limit 140
Yaw Gain 100%
I tried recalibrating the Controller and it didn't help at all. It doesn't seem to matter if there are low winds or higher winds, low speed or high speed flight, lens hood or no lens hood.
Another related issue is centering. If you are yawing to the left a bit and then release the stick to center, it wanders back to the right slowly about 5 degrees and then stops.
I am wondering if the gimbal yaw motor is the issue but I don't really know what the symptoms are for a bad yaw motor.