If you can get Butler for anything other than Rudy and Donovan you do it.
I would try something like Joe, Burks, Sefolosha and Udoh for Butler and Dieng. I love Joe, but if you can get a top 15 player for him plus rotation players you do it. Dieng is overpaid, but he is playable and would be especially valuable if either Rudy or Favors miss time this year. As for Butler, I expect he will sign with whatever team can offer him 5 years. That contract is too long, but you could probably move off from him in the next 3 years if you wanted.
This Jazz team's window to compete is small. Rudy turns 27 this year. He is probably going to be at this level for no more than 4 years, and then fall off considerably (he is a big who relies on quickness/athleticism rather than power and skill). You bring Butler in this year and your top three are championship level (1. Butler, 2. Rudy, 3. Mitchell). You lose depth, but your top 9 are still really good. As Butler declines, Mitchell will be rising, so they can still provide a competitive top options (1. Mitchell, 2. Rudy, 3. Butler). I think you go for it because it could buy them FOUR YEARS of championship contention (when was the last time we could say that?).