I forgot to share my method; I got tired of applying the Aramith polish by hand and I really didn't want to buy an expensive ball polishing machine.
I use my Dewalt variable speed buffer set to it's minimum 600 RPM. I use a Meguiar's W8000 Soft Buff 8" Foam Polishing Pad on the buffer. I place the buffer on the floor pad side up, sit down and throw a leg over its handle. I then power it on and place a pool ball in a travel coffee mug (with a diameter of about 2-1/2") that has a microfiber towel in it. Then, I flip the coffee cup over onto the spinning pad (near the center of the pad with one drop of Aramith ball cleaner/polish) and apply just enough pressure to spin the ball so it gets polished evenly. I pull the coffee mug away from the center of the spinning pad to increase the polishing effect (speed) and move it in to the center to reduce it.
Make sure you feel the temperature of the newly polished ball to tell you how you did. You should feel that it has a warm, even temperature. If you have hot and cool spots, you need to lighten up on the pressure when you push the cup with the ball into the pad.
This takes me about 10-15 minutes to have my Aramith ball set playing like new. The best part is I had everything I needed to do this in my garage already and I didn't have to fabricate anything.