From the above dimensions were talking .120 taper per foot which may be close to the appropriate taper pin reamer. Driling the case out .005-.010 undersized and then the reamer with a stop on it would give the tapered hole. But it would still need to have the top counter bored for the rim.
If you know someone who works as a machinist tool maker or best a cutter grinder, a 5/16 drill can be modified with a smaller drill/ pilot 1/2"-3/4" long ground on the end then the step sharpened and the pilot sharpened. also shorten the drill as much as possible. this will do both in one set up and stop setting. the webless pilot holds sie fairly well as it tends to burnish the last little bit. I have some counter bores and other tooling made up like this. Saved set ups tool changes. If this route is taken make sure the angles and reliefs are for brass to avoid grabbing.