About 3 years ago I moved from Seattle to Austin. I had a bunch of guitars and basses, and here's what I did:
Each guitar/bass was in its own case or gig bag.
Each case or gig bag was then packed into it's own cardboard guitar/bass shipping box (you can usually get free boxes from your local Guitar Center, though it may require a little dumpster diving).
I then bought some large wardrobe boxes from a local storage facility. Each wardrobe box could hold 5-6 guitar/bass boxes.
So, when it was all said and done I had 4 of these large wardrobe boxes, each one containing 5-6 guitars/basses, each guitar/bass in its own box and in its own case or gig bag.
No mover, or anyone else looking at the wardrobe boxes, would have a clue what's inside. And it would be a real challenge for someone to try to run off with one of these wardrobe boxes. And I had peace of mind that my instruments were very safely packed and unlikely to be damaged.
I used U-Haul's U-Box service for my move (kind of like PODS), which worked out great and was a lot cheaper than a moving company. But I would have packed the guitars and basses the same way regardless. I didn't have any tube amps to worry about. I did box up my amps and speakers cabinets as well though, not in wardrobe boxes but in seperate boxes for each amp or cab.