I have similarly had good results saving them in a bag of dry peat moss in the basement over winter, then potting them up in the spring. I have never cut them into pieces though. Last year, after drying them off and dusting off all the dirt, I wrapped them in Saran wrap until January, then in planted them in pots of dry seed starter mix andkep them in the basement. In spring I wet the mix and brought them into the light and they sprouted. It took longer this way though. I don't think it matters if they're roots or potatoes. I think potatoes are just thickened roots?

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linnea, I just posted an answer in the Annuals forum (Home, but in that winter sleep, zzzz...). Basically the same answer you got here. The main thing is keep them dry enough not to rot. I cut the sprouting ones in pieces in the spring and let them dry before potting up, though sometimes they rot anyway. If you have more than one tuber, you might try both ways. If you do, report back! :)

Christy, How did it hold up?