Remember, Atlanta's cheap. Perk would likely walk next summer, they'd have his services for a couple months (and they already have Horford, they aren't lacking for a good center). Big Game Davis isn't that much of a trade bait. 'Sheed's expiring contract isn't any more attractive on a cost-savings basis than just letting JJ walk.
So, it'd be a half-season of Perk, plus BGD. I've got to believe that they can get more than that in a S&T for JJ.