John's right, just got down here the Big Easy

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I had the movers take some gear, the higher value stuff I took myself in a Uhaul. We were fortunate, we were able to work out a "door-to-door" with the moving van, so we didn't have to screw around with stuff being mover on and off trucks, storage, etc. I think that's where most damage tends to occur.
I took my Rics, acoustics and some other guitars that I was concerned about in their cases, on a cushioned floor (I had 3 4x8 sheets of plywood with foam sound tiles I had used in our old condo, laid them down as a "soft" floor in the 14' Uhaul. I also took my Fender '57twin and reverb unit. I had the movers haul a couple solid state amps, a set of edrums (though I disassembled and packed them in one of those big plastic tubs), and some lower end guitars.
I loaded the cases and harnessed everything to keep them from shifting around.
Only things I was kind of worried about with the Uhaul were the security of the truck during an overnight stay (remedied by deciding to stay at my sis-in-laws), and heat build up inside the truck. We got down to NOL on a Sat, and weren't getting the keys to our house until Monday, so the truck had to sit for a day. I checked it periodically, and while the inside was warm, none of the stuff in the truck felt hot to the touch.
Whether by luck or design, everything arrived in great shape. AC in the new place keeps the humidity in the mid-50s, though it has gotten near 60 once or twice. Just to be on the sage side, I picked up a little 25 pint dehumidifier to help as we move in to the heat of the summer. All things considered, I prefer dealing with a little too much humidity as opposed to the dryness in the winter back in NVA/MD.
Good luck!!
Bill