Cool and dry works for me Rick. 55-65F. Some hybrids like 'Picasso', Z. rehmannii (lance leaved pinks) and Z. elliottiana hybrids (yellows) I have tend to sprout "early". These I store on my basement steps where it's cooler. Definitely a tripping hazard but it's the coolest spot I have. Some sprout so early they're difficult to plant out without damaging the new growth. The new growth also seems to be more subject to cold damage once planted which inhibits or distorts bloom. Note that between lifting and planting is +-6 months here.
Rhizomes vs. tubers
FYI The Kew WCSPF lists them as rhizomes mostly, other sites as tubers.
As to moist vs. dry - I don't know. I've never done moist and dry works even for my extended storage time.
When or whether to lift looks to be a bit complicated. Basically these are
dry season dormant plants where they naturally occur, southern Africa. Cold hardiness is only part of the equation. In Florida for instance, well within the cold hardiness limits of all Zantedeschia,
this article notes only the evergreen Z. aethiopica are reliably perennial. I'd surely enjoy hearing how hardy folks find Callas in various climates.
As I've been way less diligent about lifting my Callas in the fall lately, I find more tubers overwintering. The plants generally aren't robust and have few if any flowers. Those planted where I
heavily mulch Musa basjoo do best.