Thanks for your thoughts and input. Yes, I also saw the lack of any points being exactly on target. I'm still wondering how that might happen. For directions, I thing having the GNSS antenna on the rear of the drone is part of the answer.
I agree that surveyed GCPs would be the best solution to this issue. As you also mention, a local real-time GNSS corrector system like RTK tailored for drone operations is an option. Either way means a significant increase in equipment and labor costs. I'd be interested to finding a way to include WAAS/SBAS signals to apply a real-time corrector. I'm still looking for that.
It would also be nice to have a way to post-process the drone GNSS data (like most GPS receivers/software can do), though I haven't been able to find anything online to do this. If nothing else, a person might want to know the directional bias and perhaps find a way to account for this error.
But for those that don't go either of these steps and just use the drone's position for aerial mapping/GIS, this is a serious issue to be sure. From my days as a surveyor for NOAA, the rule of thumb is that your positioning framework should be 10x more accurate than the final geo-spatial product. Using this as a guide, a 2-meter uncertainty in the framework would mean the final product accuracy would be only be good to 20 meters. Now we are talking something a bit more troubling.