I was walking through the big orange store today and saw something that caught my eye, it's called a Bucket Head. It's a mini wet or dry shop vac that works great for cleaning out the ash from large eggs. The hose is small enough to fit between the fire box and the base to clean out the ash, I pushed to about a 3rd of the way around from left and right. I haven't tried it on the medium or my mini but, I'm reasonably sure it will get the ash out from underneath the fire grate on all of them.
It costs $19.97.