Upgrading from my Kx to my K-30, was a big improvement in focus with the 55-300. While I waited 3 months for my repair on the K-30, I decided to go for the K-5IIs, and again much improved focus on the 55-300. I don't shoot much BIF, but use it mainly for sports like rugby and hockey. I understand that the K-3 is even better at focusing....
I use my K5IIs mainly with the 55-300, and my K-30 as backup, with WA and short tele lenses, and with manual lenses and focus peaking.
It must be said that the 55-300 is notoriously slow in focusing, so just another lens like Sigma 50-500 or such might be better, or the DA300* with the new 1.4 converter, but unfortunately I don't have them, so can't really comment.