Over-Wintering Spider Lillies

I grew 3 hymenocallis Spider Lillies this year. It was a bit of an experiment as I thought the weather where I live would be too cold and wet for them to succeed here. However, they did and they were splendid. However, they will not last over winter as temps will be too low and the ground too wet.

So......... I have lifted the bulbs today and am looking for a bit of advice. Should I let the bulbs dry out completely and then start them again early ext year in pots? Or should I pot them up again just now.

I have the bulbs drying in a cold frame and had intended to pot them in early next year and keep them in the frame. But having seen how tuberous the roots are, I am concerned that they may rot.