I've found that if I drag a display cabinet into Household Inventory it will take all the items on that cabinet into household inventory. They will not be on the cabinet when you bring it back out, either at current home or at new home, but they will be in the inventory so you don't lose them. All you lose is whatever layout of items you had tehre - for example if you had all the varieties of cut Yellow Sapphire on one cabinet, all the Rubies on another. You'll have to sort them out again. I do this regularly because the things seem to get bugged after being used for a bit.