The DA 560 is a great lens in many ways, but the K-3iii instead of making it better highlighted its cons. It is the worst tele-lens in terms of AF tracking capabilities. The DFA 150-450 is a joy to use, while the DA 560 needs concentration and effort to fully utilize it. I have found many things while playing around with the K-3iii these last days using the DFA*70-200/2.8 (sometimes with the 1.4X TC), the DFA 150-450 and the DA 560. The DFA 150-450 is the telephoto lens for the K-3iii offering fast AF, great tracking and a lot of reach. The DA 560 is not much faster to AF on the K-3iii and while when the AF is spot on the IQ is impressive, it is difficult to follow BIF (in circumstances where the DFA does very effectively) and also the camera seems not to cooperate so well with the big lens. 2-3 times it stuck after I had changed some settings and I feel it has to do with the AF area that is restricted with the DA. Also sometimes during a burst the shutter/mirror sound is weaker like it didn't function properly! The images I checked where OK though, so I don't know exactly what's happening
I have made other observations too I might find the time and mood to write about but as a conclusion the K-3iii AF is very reliable and fast even in AF-C tracking but it highly depends on the lens. With the DFA* and DFA lenses it is great. In fact I can track swallows flying low and in random tracks (their usual chaotic flying style) and during a burst even if the camera loose focus it will eventually find your subject again after a few frames while tracking! The DA 560 cannot track so fast subjects and also you need to have found focus prior to releasing the shutter otherwise the whole sequence will most probably be out of focus. There are some exceptions but few in comparison to other lenses. I'm very impressed by the DFA*70-200/2.8 performance even with the HD 1.4TC! Unfortunately I don't have the 55-300 PLM to compare which I think it will be even better, unless the faster glass makes the difference in the new K-3iii AF performance, which might be possible too.