I was thinking about that last night, and I couldn't think of any way to do it that would be satisfactory. I think the best thing to do is just squeeze out as much juice as possible and replace the wick.
Well I combined two of my favorite things, the drunker and my ultra sonic cleaner. Just put the whole atty head and caddy in there with wicks still in. At first I saw a lot of gunk get knocked loose.. But the coil is still pretty icky. Unfortunately this means I have to let the cheese cloth soak all over again.. I'll let you know if it was worth the effort.
Kind of makes sense to buy a 2nd Drunker.. Jussayin.