Wow, it always is fascinating how many contorted procedures get implimented for this.
Get an annealing fixture from Todd Kindler, which is essentially a fitting that screws into a butane cartridge with a lenght of copper tube formed into a circle at the end with holes all pointed into the center.
You can do 20-25 cases at a time standing in a cake pan, etc. with water about 1/2 way up the case.
Once you fire it up you lower it over the case mouth/ neck and with a kitchen timer give it about 15 seconds, give or take and then knock it over and hit the next case and button. This is idiot proof and costs about $30.
I've used itfor everything from 14 walker, R2, right to 6 PPC cass.

Dave, your room is WAY to neat 

Frank

I use a deep well socket that whatever size case I am annealing fits in. (I like a close fit). Then take a piece of all thread 3" 4" long that fits thru the square hole in the socket , put nut inside the socket one outside and adjust all thread to let the neck stick out just past shoulder, tighten nuts, run in low speed drill, drop in pan to cool. cmargs.

I must be the maverick here.  I was taught to stand case in a pie pan of water a little over a half inch deep to protect the head from softening.  I set the pan of water on an old phonograph turntable turning at lowest speed.  Darken room. Set case to be annealed upright in the center, turn propane flame till barest color develops and tip over into the pan.  It immediately moves to the outside of the pan, next case goes in, repeat process till done.  Lots of cases can be done before you need to remove a bunch to do the next batch.   Gives absolute protection against annealing the head, and the water quench assures dead soft brass where desired.   

Am I the only one who uses this process?  I think I learned it like 40 years ago.

Above is listed most of the hard ways, here is the easy way. Just remember it is only money.
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Thanks fellas. Looks like there is more than 1 way to skin this cat.