Simple solution, make your own expanding mandrel. Take 6" pieces of wood and turn them round. On one end make them all 3/4" diameter with a 2" long tenon, this will fit your collet chuck. Turn 2" of the other end to the size you need, drill and tap for a 1/8" pipe threaded, NPT, plug. Cut the end in fourths. You now have an expending ring mandrel. Hint, drill a center hole on the end of the NPT plug.
Marvin