A few thoughts.
1) I don't see Sheed's salary combined with anything else we have to offer really being enough unless we maybe thought about including Perk. I don't think Houston is willing to give him up for just cap space when they could probably get more.
2) I agree with Chris that a third team would probably have to be in place for it to work.
3) Murphy's interesting, but given our situation at the wing spot right now, I don't love the idea of using our only trade chip to acquire another big.
But going back to #1, if we're going to trade Perk, it might work here. KG, Jermaine, and BBD could really play most of the 4/5 minutes by themselves, meaning that our 4th big wouldn't really need to play more than 10 mpg or so.
If we could upgrade the 2/3 spots that much (Battier), it might be something to think about, particularly if Danny isn't thinking he can/wants to re-sign Perk anyway.
Though further digressing, Perk's injury may hurt his chances at big money next summer.