I ordered four varieties, two hardneck and two softneck. One of the hardneck varieties is German Hardy based on your recommendation. I expect to plant after everything is killed back by first freeze, probably Late September or early October. I ordered from the source you cited. Do you have any planting or growing hints?
You’ll get instructions with your order. Garlic likes sun, loose, rich soil, regular watering and a good layer of straw mulch.
Aside from your horrible soil, you should do just fine, LOL! ;)