http://www.dpreview.com/reviews/pentax-k-3/12#Colour
DPR couldn't find an acceptable better setting even though they had tried their best to fiddle around with many in-camera colour settting parameters but in vain.
However, there might be a workaround I previously found out and proposed. I don't know if it could work for the K-3 or as it is notorious that the K-3 had even worse colour response than the K-5. But if you are a K-3 user, you can try anyway and tell me your results when my settings are applied:
My Best Optimal Custom Image (Colour) Setting Combination for the Later Pentax Digital Bodies
As for that crappy JPEG engine and sharpening issue, I think there is not much to do and deal with unless RAW is shot.