Plugs are needed to hold the inner balls stable until all the chases are cut. You can make them out of wood or a very hard, high temperature wax called 'machinable wax'. You'll need 12 (maybe 11) but I suggest making about 16 +/- to start
Styrofoam plugs - This is the simplist, easiest and most effective plug in my experience. Get some 1" foam board sold as siding insulation for homes. The stuff I get is light blue, and 1" thick. Cut it to 1"x1" squares and shape into a cone with a rasp. I can make 12 of them in about 5 mintues.
Wooden plugs - Turn cones 7/8" tall with a small diameter of 1/4" and a large diameter of 7/8". A lot of people have had luck with this, but it's not my first recommendation.
Wax plugs - Start with making a mold. You'll need a piece of wood 1-3/4" x "1-1/4" and long enough to make about 6 at plugs at a time. Cut the mold in (half the long way) and clamp it back together. Drill holes into the mold, centered where the 2 halves split, and a little deeper than you'll use on the balls. Use the same drills for the mold that you'll use on your balls.
Buy some machinable wax (it's blue stuff). I prefer the 1" cylinders, but any shape will do. Cut into smaller pieces. I find that 1" x 1" x 3/8" is about optimum for melting quickly. Any metal containers with a handle will do, but be sure to keep it on a hot pad. I use an embossing heat gun, but anything will do. Just make sure it can reach 325' but be sure to not exceed 400' (you don't want the wax to ignite).
Once the wax is melted, pour very carefully into the mold. Do not get it on your skin, as it will burn severely. It should be cool enough after an hour (maybe 2) to pull the mold apart and start the next batch.
When you're done with all the operations on a primary hole, insert the plug into the hole and push it it into place or tap gently with a very small hammer. Turn the plug to fit flush with a handy turning tool so that the chuck will hold it in place after the ball's turned to the next primary hole. When the ball is completed, push or pick out the styrofoam plugs or drill a small hole near the center of the plug (for wax or wood), insert a screw about a 1/4" and pull out gently with pair of pliers. I usually throw away styrofoam plugs. Wooden plugs can be re-used several times and wax plugs can eventually melted back down and re-molded.