Debbie, perhaps I can help. I am in NE Mississippi and in zone 8a, and like you, our winters are pretty cold and very wet. I grow both 'White Butterfly' and 'Shampoo' gingers, and have lots of it. I leave my plants in the ground, cutting off the tops in mid-late November, approximately 4" above the soil. For those rhizomes near the house, I do nothing more. For those out in exposed areas of my landscape, I cover with 4-6" of oak leaves. For those rhizomes in pots, I will remove them in November/December, shake off the soil and put them in cardboard boxes. I put a 2" layer of shredded paper then the rhizome(s), another layer of shredded paper, more rhizomes, etc. These boxes are put on my enclosed, heated porch for the winter months. They will be re-potted in the early spring. All my gingers bloom in the summer, regardless of where they are growing so I don't know why your's did not bloom. In fact, I have so many rhizomes in the spring, that I sell a good number of them.
You will want to be careful when storing any plant or rhizome in an unheated garage. If the temperature get cold enough, they will surely freeze and die. I lost all of my Plumeria that were stored in the garage and in the attic a couple of years ago when the temperature got into the mid-teens. I now store no tropical plant in either location. It is just not worth taking the chance.
Ken Ramsey, Certified Mississippi Master Gardener
