I would store them as you would dahlias. There are a number of ways, but I like the saran wrap way. Just do as you were going to, but wrap in plastic before storing. I used to put mine in a cooler to store them. Protects them from any critters as well as moderating any temperature fluctuations.

Glad you mentioned critters -I tried storing SPV plants over the winter in the big clay pots I'd grown them. Put them in in my open garage (it's very old, and the doors slide, but are not tight when closed). It turns out the tubers are very attractive to animals; they were all dug out of their pots - and gone - when I checked them a few months later. A cooler would probably not have fared too well, but a steel trash can might have done the trick.