I've had good luck with cane/rhizome cuttings. I haven't had any luck with just the leaf, but did not put a lot of attention into it either. It should be no problem dividing but I would go for the cuttings. The past two winters I've kept it in the garage where it drops all its leaves and the canes as well leaving just the rhizomes at soil level. This year I am keeping it in the basement under lights to see what its behavior is.

Here is my newest cutting (2 days old with spider)
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Here is a comparison between the Mother (3 years old) and a daughter from this summer
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Another view
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Butch