Since Papelbon will want to "set the market for closers," which is making is less and less likely that he will stay with down year (by his standards), it would be nice to get something for him other than 2 draft picks when he walks. Bard may not be completely ready for the closers role, but having him for the next few years (especially cost controlled) over 1 more of Paps is worth trying to swing a more difficult 3 team deal. As far as the third part of this three way, possibly the Braves with the retirement of Billy Wagner or any other team looking for help at the back of the bullpen would work. It may require more work for Theo and a few extra minor prospects, like a Reymond Fuentes serving as the concealed $20 bill in the consummating handshake, but having Bard close out the 9th inning at Fenway for the next few years is worth it. 

I really don't see the D-Backs taking Papelbon, as they seem to be in a "Shed as much payroll, get as much talent as possible" type situations.

So I really can't see see them taking a closer that is hoping to "set the market"

Which is why a 3rd team would need to be involved so Paps could be flipped for someone more desirable to the Dbacks. Possibly get a young starter close to the majors, if we don't include Doubront (not mentioning Buchholz, who I wouldn't trade straight up for Upton), which AZ might be looking for. Haven't looked into it too much, and just throwing a name out there, but how about Jair Jurrjens from the Braves?

Maybe something like:

Red Sox trade: Jonathan Papelbon, Jacoby Ellsbury, Lars Anderson, Yamaico Navarro/Jed Lowrie, and Reymond Fuentes/Che-Hsuan Lin
Red Sox get: Justin Upton

Diamondbacks trade: Justin Upton
Diamondbacks get: Jacoby Ellsbury, Lars Anderson, Jair Jurrjens, and Reymond Fuentes/Che-Hsuan Lin

Braves trade: Jair Jurrjens
Braves get: Jonathan Papelbon, and Yamaico Navarro/Jed Lowrie

I'm not too sure on the Braves situation (although they seem to have the young pitching to replace JJ), but I wanted to see what people thought.