Generally the Hedychiums are the hardiest.

I have a Hedychium that has been hardy for me with mulch is zone 5b for 10 years. It is from sikkim and looks like a spicatum

red button ginger or lipstick ginger as some call it

Have you tried planting the ginger you can purchase at the grocery? I can grow it, with protection, here in Virginia. Perhaps if it was potted?