That Cresswell book is a great source but unfortunately all of the recipes are based more on the old style of doing root beer, using sassafras, which is ok but if you actually try it sassafras tastes significantly different from modern rootbeer (like a&w).
Modern stuff is made with wintergreen as a primary ingredient (peppermint and spearmint are not a good alternative, I've made that mistake

). I've gotten my best results by using wintergreen oil, anise oil (which provides the other big flavor, licorice), vanilla, and nutmeg oil seems to provide a little something. You have to use food grade oils, and cut them with alcohol or some other food grade emulsifier like propylene glycol in order to mix them with water, and you use *very* little oil, like a drop per liter or less.
I've been trying off and on for a while to make a good root beer recipe, and I've had some decent success. I like it, my friends like it, but you can tell that it's homemade (although it does taste like root beer).
I haven't had much success using actual roots and barks though. They always seem to leave that root or bark flavor in the final product and I can't seem to reduce it enough to enjoy the drink.

I think maybe the old timers just dealt with it, and I've been pampered with root free flavored A&W all these years.
http://www.rootbeerbrewer.com