He would probably not consider Barker and Bogo, but Martin and Bogo maybe. I would go for that one, and its worth a try. However, I doubt he makes this trade. Who are your other D?
I'd start with Barker and Bogosian for Weber to see how he reacts. Sometimes gms value players completly different, so even this is worth a try. If he rejects you can still offer Martin and Bogosian, this would still be a good price for Shea Weber!
He rejected Martin-Bogo, though he has mild interest in Bogo (none in Martin). I've submitted a number of names I'd be ready to move. We'll see if he comes back with anything.