Yep, the larger the tubers the longer you can overwinter them. They need a few months rest no matter what temps. I keep them dry in pots and when I see little shoots starting to appear I lift them out, clean them up (small ones can dry rot easily and don't survive well) and then I usually put them in very moist sphag on a heat pad to sprout roots and then I pot them up and they sprout leaves in sunny window in NJ in April-May. They need temps at the roots to be above 65f at all times. But 70-80f is better for growth, so I don't put them outside until mid-June usually.
I am wintering in So FL so I decided to experiment and brought them over and they did not decline insep-Oct as usual , but around mid Jan, as the pots were outside and temp were 80/65-70F until then. I think that brighter light levels and higher temp with higher humidity all helped them to decline much later. They woke up in March and by April were going strong outside (but mar is already 80f here). So this past year instead of 6 mo in NJ they grew for almost 10 (with summer in NJ and then back to FL👍😁).