I know this is Brian's thread, but I do have a lot of input to this question as I just finished shipping my livestock from Washington State to North Carolina, with pretty disastrous results...
I had two rocks on top that had a lot of my favorite corals encrusting really well on them (ORA Red Planet, for one). I figured i didn't want to lose a years worth of encrusting goodness so I got giant, thick bags from my LFS and tried to ship those two rocks in their own boxes with a lot of padding around the rocks to stop them from shifting. They looked sturdy enough, but Southwest Airlines (the freight division) ended up crushing both of those boxes and then refusing to ship them on because they were wet. All of my prized corals ended up dying because they sat in a warehouse cold and dry for over 48 hours...
Moral of the story, moving sucks but you just have to accept that and move on. If I ever did this again I would frag all of my corals off the rocks, frag any big ones at least twice to ship in separate bags, and ship all corals in their own bags. Definitely give some corals to friends with local systems so they have the means to repopulate you if something goes horribly wrong. I would only take what fish were special to me and sell EVERYTHING else. I shipped a box full of liverock (the freight price was that good) but I think it might be what caused the boxes to get crushed in flight.
Good luck! Moving is already stressful enough moving a fish tank can be downright awful.