Here is what I invisioned for the folder type of view. Basically, instead of having tabs, you would have multiple bags like shown below. They could either open up in new windows like the existing bags do, or open up right in the inventory panel, with a button to go back to the top level.
The armor would open up an armor bag, and the weapon would open up a weapon bag. Each bag would have it's own icon, I just didn't feel like making them.
The only problem with this type of layout, is that you can't see everything that you've pulled all at once, since each item will go in a specific bag. The only way around that would be an icon to show everything, in a sortable list.