Replace Sonny Gray. offer more years than you like to Nola, Montgomery, Eduardo Rodriguez or actually Sonny Gray. I'm a gambling man, so I'd roll the dice on Giolito too, though I have a feeling he's going to be a much talked about and devisive free agent this winter.
Cut the offensive Ks. The biggest problem here, is that it's hard to tell if it's the players or the hitting philosophy. Do what you like with the coaches, but from the hitter angle, this isn't all that tough. There's really only seven hitters with obscene K numbers. We're stuck with Buxton, so no use worrying about that one. Cutting bait on Gallo and Garlick should be easy enough. Michael Taylor became a bit of a cult hero around here, but his Ks were just too much. Find our CF defense somewhere else. Then you have Julien, Larnach and Wallner. Julien is the best of them and also seems most likely to improve, so I'd keep him and look to move both Larnach and Wallner. Getting rid of those players would have dropped the team's K% from a league worst 26.6% to 24.3%, isn't great, but not league leading bad. If one was so bold to move Julien too, the K% goes all the way down to 23.7%, which is solidly middle of the pack.
To get that lower, obviously the replacements need to be good at putting the ball in play. The easy part is when they turn to the rookies, don't fart around, call up Lee and Martin who are the best at this. Kiersey and Prato acceptable. Maybe avoid Severino and Chris Williams. The harder part will be the free agents. Most of the best ones will have some strikeout baggage. I don't know that this team really needs offensive free agents though. If they can make a CF option out of some combination of Buxton/Castro/Martin/Lewis, they can probably roll with what they have internally.