On my A6300, because the 'tracking' didn't really work (Lock-On AF wasn't quite up to fast birds), so I just used AF-C and wide, and set priority to release. That did the trick most of the time - I found it better to let me decide when I got focus as there are times the camera might not have identified a good focus and not fired the frame. I'd get occasional misses, but not too bad.
When I went to the A6600, and was able to start using Real-Time Tracking AF, which actually DOES work, I was originally going to use 'release' but I had it on Balanced for the first week or so and was very happy with the camera's performance - so I ended up leaving it there. I have never experienced the full refusal to shoot that 'AF' priority can...