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A relatively stiff-bristled brush (a small paintbrush is pretty common to use) should do the job fine, you're just trying to remove any old coffee grounds that have lodged themselves in around the burrs. If you haven't done it in a while, you might need something a bit stiffer (I've got some nylon-bristled brushes for cleaning the grouphead on my espresso machine that work great)
My Rhino and Porlex never really got too bad. Not sure if it's to do with my Sette being used for finer grinds, or the larger burrs and speed of the motorised grinders.
Yeah the flipped direction is a bit counter-intuitive. Easiest way to remember is that when you screw in the bottom bit, it's in the direction of finer.
On that note, clean your grinders folks! One thing I love about the Sette is that I can change between the filter and espresso burrs in less than a minute with no tools. Damn handy design, also means cleaning is super straightforward.