The fact that they have a top 15 pick would suggest to me that while they may not amnesty him, they can however add him with the pick for a trade to get someone.
Or draft someone like Steven Adams and train that player up behind Perk. Let him take Perk's place in the starting lineup in two year's time to balance the books better.
Given where they're drafting and their need for short-term help as well as long-term help, I could see them being very interested in Dieng or Plumlee too, or maybe even Withey. I think those guys will be able to give them more, immediately, cheaply and for 4 years guaranteed, than any big guy they are likely to acquire via trade.