Dave, will the crates be sealed up prior to the movers showing up?
If so, I'd suggest you wait, that way if the movers do the final "sealing," its considered carrier packed, so if any damage occurs its the movers fault, where as if you have it packed and sealed, its owner packed, and any damage they are not liable for. I've seen guys I've work with have TVs shipped in the original box, that they taped up prior to the movers coming, they were liable for any damage, so when they PCS'd and got to the new base, and the TV didn't work, they were screwed.