Here's a possible move with some risks and rewards. Trade for Ian Kennedy and Wade Davis.
The Royals tried attaching Kennedy to Davis before we went on the DL. They're looking to extend guys like Hosmer, Cain, Duffy, and Moose and the Kennedy contract is hurting them. He has an opt out after 2017 that would cost $6M. If he doesn't opt out after 2017 you'd be on the hook for 3/49 for 2018-2020. If he does you just bought a comp pick for $6M.
Wade Davis has a flexor strain, which is muscle and not ligament. If he comes back healthy and pitched like he does in his contract year for us next season, we could have one of the best closers to trade next July, and we've seen what those fetch on the open market.
Best case scenario, we have Kennedy for a season, pay him $6M to hit free agency again, and get a pick. We also get two-three key young players for Davis in July.
Worst case scenario- Kennedy sucks it up, we're on the hook for another 3/49 and Davis goes down with injury.