I'm no expert but, will give what advice I know.
I live in zone 8, NW Louisiana and grow white butterfly ginger. You should be able to dig and move them as soon as the stems start to die back.Replant them at the same depth. These gingers should do fine in your area also, they smell awesome. Spread like crazy and preform best with moist rich soil.
They are really hardy and should do fine when moved around. If you are nervous though, just leave a few behind so you'll have extras until you see them growing in their new place. You can also transplant in spring .
Pattie

I have one to sell or trade that is decidious. It is a white with a flush of pinky-coral in the middle blossoms that are fragrant. It will grow from rhizomes in one season and bloom in August. Now they are starting to go yellow and in a month the tops will be dry and come off with a slight tug. I know it is a Zingiber but I'm not sure of the species and will go back to the UC Botanical garden to find out. This ginger would be good for those in areas too frosty for regular ginger to grow and bloom.

To brianbruning: you said you have a ginger for sale or trade. The only thing I have for trade right now are ripe datura metel seed capsules (large seed capsule opens when ripe, containing hundreds of seeds--fascinating). Interested?