Thanks for all the input!
It seems like the most widely held opinion is that gravity-fed bins will always have the potential to jam.
Realizing this, I think my best bet is to make some kind of agitator (probably like the one drawn by BurningQuestion).
Despite my preliminary misgivings I am beginning to see how using an agitator might actually be easier than redesigning the bin.
Based on people's ideas (and the bins of other robots) I created a CAD model of the new bin. It is similar to the bin most people thought was least likely to jam (bin #2), with offset angles (as recommended by Jonathin Norris).
Looking at the design I am already beginning to see new jamming issues. There is also the problem of how to transport the plastic to Atlanta...
Overall it looks more difficult to build than an agitator, which is probably what I'll wind up doing.
Does the new design look workable/less likely to jam?