If we could go back in time to around 2002 and trade Sheed for picks and a young big, would you do it? Personally, I probably would (and I was a huge Sheed fan). Add in that Hickson is a very serviceable starting PF (but a lousy starting center) who will walk away for nothing, and yeah, I can see a good argument for parlaying Aldridge.
Hickson's stats aren't as good as his actual play, but you have to remember he's only 24 and has been playing out of position at center for the majority of his NBA career. He's a high percentage scorer and a fantastic rebounder. He just needs to play at his natural position. And he needs to work at developing some offensive moves.
I'm not desperate to unload LMA, but Hickson's weird contract situation and his ability to give you a lot of Aldridge's productivity at PF make it a viable option. Has to involve a good center and a very nice pick coming back, though.