I've never pulled the fire ring so I will do that today. I clean the bottom out damn near everytime and I make sure there's no ash in the leftover coal by stirring it up real good before adding more.
Clean by taking out fire ring next up. :0008
Yeah - be VERY careful though - you drop it and it cracks or breaks - $$$$$$$
Take the fire box out as well.

And take out the metal grate. Should do the trick.