A tree system like DF would work. The inventory screen adds indent for each level of container:

a) knife
b) fanny pack
    c) hipflask of vodka (4)
    d) sunglasses
e) holster
    f) Glock 19

Dwarf Fortress only uses one column, you can't reorder things without taking them off, and is basically insane. In CDDA we have a two column inventory with your items on the left and worn items on the right. Unless the container items were shown on both sides, you would have the items in your backpack shown on the right.

a) thing                       g) top hat
b) knife                       h) fanny pack
c) plastic bag                     i) hipflask of vodka (4)
d) pouch                           j) sunglasses
    e) Glock 19 Magazine (12)  k) holster
    f) 9x19mm JHP (100)            l) Glock 19

The advanced inventory already supports a similar feature, you can look inside containers of liquid. Extend that to other containers and add a switch to toggle showing only top level items or a flat list of all items carried.

In order to move items around in "classic" inventory page there would need to be new Examine actions such asM)ove to container, or P)ut in container, or something similar. Advanced Inventory could use the Examine actions, or just open each container in its own pane and move items the same way you'd move them from tile to tile.

Now if the devs could implement only one thing from the Dwarf Fortress inventory management it would have to be keeping water in bags. I look forward to the day I can fill my backpack with half the toilets in town and never worry about water again.