Parker,
If you take a look at the Tutorial on Making Closed Reed Predator Calls you will see one way of doing it, which sounds a lot like Braz and Dogcatcher do.
SInce 99% of the closed reed calls I make are two piece calls, I turn the mouth piece in a chuck, drill it to 9/32 and then taper the inside of the mouth piece with a step drill. Once that is done, I sand out the ridges to get a smooth tapered boar. This seats my read down in the call about 3/4". Of course on the bonkers the reed is set very deeply in the mouth piece. You do not want your reed to be sticking out of the mouth piece no matter how you do it, and recessing it a bit is a very good idea.
AL @ THO