The KP is pretty capable - as good as the K-1 with respect to AF tracking in my experience. No doubt the K-3 Mark III will be even better, possibly considerably so.
The Sigma 17-50/2.8 HSM worked well for me while I had it, but it was several years ago (back in the K-5 days). I couldn't recommend the DA* 16-50/2.8 over it (at least for AF - I loved it optically), but there is a new PLM version in the pipeline.
The Tamron 70-200/2.8 is screw drive, and I'm sure you'd do much better with the newer Pentax offerings. If f/2.8 isn't crucial for you, the DFA 70-210/4.0 is very quick focussing and works beautifully on the KP. If you need f/2.8, the DFA* 70-200 is a beast - in both size and performance (and price).
I absolutely love the DA* 300/4.0, but AF is certainly sluggish. The DFA 150-450/4.5-5.6 is superb, and has AF buttons around the lens barrel which is very handy when shooting birds in flight, etc. If you don't need all that reach, and are happy with f/6.3 maximum aperture, the DA 55-300 PLM is possibly the fastest focussing lens Pentax makes.
Choices, choices! The ball's in your court