+ 1 on fear and loathing.
I've not been able to shop for my movers, who have been vendors who worked with my employers.
Some loss and damage in all cases, with variable luck on the insurance: some vendors quickly made it right, but the last one kept demanding "further documentation" 'till I gave up (right up there with the company that cancelled roadside assistance on my vehicle because I used it).
That said, my audio gear, always packed to shipping standards, has always come through OK.
But nothing too big or complex. If I had really high value or delicate kit, I'd think the most reassuring solution would be to rent a van and move it myself, maybe with the help of occasional labor on both ends.