The company should absolutely do the packing. Then it is all on them and they have insurance. I have moved a lot, regular move, and they crate the things that are delicate, very large, or easily broken. They know what they are doing. If not crating, they have all the moving materials to protect the item. An art moving company will even be better at this sort of thing than the usual guys I deal with. The person in charge of the two or three man team usually has a lot of experience, they know what they are doing. You can watch them pack it up if you have concern about the packing.
I have had very very few things break in my many moves. Also, during my moves they have me list the “high end items.” Again, regular movers. Those items they can check over more thoroughly, list any scratches etc, and then if on the other end, God forbid, they have harmed your item there is a good record. When I ship my luxury cars you should see everything they mark on the sheet to protect themselves. But, it really does protect you too.