I just place them on a paper towel, mouth down, as shown in my previous post. That dries them overnight, or whenever the towel is dry. I placed a few on a sponge today and they dried even quicker (an hour or so). The sponge (or towel) simply wicks them dry. Before placing them on a towel (or sponge) blow the excess water from the flash hole from the primer pocket side. If the flash hole is plugged with water, the case interior won't dry completely. I should probably write up my entire technique. Not terribly complicated. I just need to do it.
"I have a love interest in every one of my films - a gun." Arnold Schwarzenegger