I would like to propose an option for items in a chest. In addition to the list of players in the assignment pulldown add an option for "Put up for roll." Once an item has been "Put up for roll" a party wide notification goes out via party chat and all members have 30 seconds to click on the item in the chest, which auto-generates a roll. Who ever wins the roll automatically gets the item re-assigned to them.
2 "optional" additions...
1) A variant (check box or whatever) that would allow you to put an item up for roll only for appropriate classes. That could, of course, get very sticky.
2) Make items re-assigned via the roll mech in the chest unable to be re-assigned. To try to cut down on friends rolling for the sake of re-assigning to their buddy in group.