Could the arrows from the 'contextual taskbar' be added to the properties panel to rotate through the generative variations?
OR~~~ a keyboard command to rotate through the options?
The 'contextual taskbar' is annoying since it's always on the screen covering other things up and can't snap into the prexisiting panel system to keep it in a place you want. I have yet to find a spot to pin it where it doesn't get in the way and have to be moved at some point.