So the output from your ballistic program shows the same correction regardless of direction of fire? It is my understanding that programs with a correction for Coriolis have an input for bearing and I would wonder why they have this if it makes no difference on the correction?
Yes - it does for the horizontal component of Coriolis drift.
The input for the bearing of the direction of fire (Azimuth) is necessary to determine the vertical component of Coriolis drift, because the vertical drift is maximized when shooting true east or west (90 or 270 degree bearings - parallel to the earth's direction of rotation). The vertical component of Coriolis drift diminishes to zero vertical drift when shooting true north or south (0 or 180 degree bearings - perpendicular to the earth's direction of rotation). Latitude is essential and required to calculate both the horizontal and vertical components of Coriolis drift. The bearing of the direction of fire (Azimuth) is only required to calculate the vertical component of Coriolis drift. (Ballistics software programs might require the input before calculating the horizontal component, but the LoadBase3.0 software yields the same magnitude of horizontal Coriolis drift no matter what bearing I enter.)
What hasn't been mentioned is that in the Northern Hemisphere, horizontal Coriolis drift is always rightward. But in the Southern Hemisphere, horizontal Coriolis drift is always leftward. So in the Northern Hemisphere horizontal Coriolis drift is additive to the bullet's rightward spin drift, for a larger combined rightward drift. If we took our right-twist rifled barrels to the Southern Hemisphere, the bullet's Spin Drift would still be rightward, but the Coriolis drift would now be leftward, offsetting and reducing the combined horizontal drift.