Looks like they've got some bad Funnel Flow in the hopper. Mass flow is probably the desired flow regime. Using a non-conical hopper is probably a better idea and would negate the vibration, which can fail.
Typically only change the shape of the hopper in one direction at at time as you move down. This often leads to hoppers with an exit that is a slot and not round.
We've used these powder consultants before and I took a week long course on hopper design: http://powdernotes.com
Edit - another method we use to create empty-able hoppers: fluidization. Not sure if this fits with your processing strategy but it also mixes the powder somewhat which prevents size segregation of the particles. And this video is pretty cool: