Try attaching string to the end of the dowel segment with a screw, and then tie the other end of the string to a belt or belt loop on your pant waist. Be sure the string is long enough for you to perform the drop reverse-roll, yet short enough to keep it from hitting the floor.
The string obviously allows you to more easily retrieve the dowel for use on the next glass or keeps the dowel from doing damage to floor surfaces.
