There are a large number of Alpinia species (about 150) and a few of them are hardy (though most of them are certainly not).
It seems a pity not to grow those that are prepared to make the effort.
This one, from Japan, is hardy, but low temperatures will prevent flowers forming on the second year canes.
I got it from Paul Barney at Edulis, and it has made a delightful lush foliage plant.