Jim,
You don't even have to unscrew the packing nut. Just measure the OD of the threads, subtract 1" for the shaft, divide by two, and then go down in size about 1/16.
Most packing you'll find is square, but a friend gave me some stuff called Keystone packing - it's kinda keystone shaped. When you wrap it around the shaft, the small side goes against the shaft. When it's bent to the radius of the shaft, it becomes square - like magic. I think it's made by the Goretex folks. US Navy uses it on the reactor feed pumps.

Al