Just turn an appropriately sized cheap plastic pot upside down inside the large- and medium-sized pots and pour soil around them. This creates a platform for the next tier and saves money on potting soil.
Dream State: Grow Your Own Ginger At Home - start it indoors early in the season, as a houseplant. Then move outdoors into your garden in the spring. Every "finger" of the old root will produce a new ginger root.