I'd say you should get it out of the ground in the spring, before it breaks dormancy. In a pot for the winter you run the risk of it dehydrating, or getting its roots frozen and killed. Good luck! I think they'll survive being moved no problem.

Alberta - I have had real bad luck moving daylilies when it is hot. They really struggle and I have lost a few. If you can wait until fall, it would probably serve them better. Rita lives on LI too, so maybe she can speak to this better - as she lives in the same area.

I divide mine anytime during the summer. Just do it early morning and put in shade a few days to recover or do it late in the evening when it's cool. Water well. The foliage may look limp just cut it off. It will have new growth in a week or so.

"It is much too hot to work out there and I may wait until late August/early September. Is that enough time for them to get ready for winter? (Zone 5)" Yes. In fact fall is a far better time to move things than summer. And if it is too hot for you to work outside it is much too hot to transplant plants. They suffer from the heat as much as you do and this in addition to transplant stress can set them back. "Should I dig them up and set them out to dry a bit as with Irises? Maybe I can take a day or two to reset the bed while they are removed." I would not let them sit out- in this heat they would dry out. Even in the fall I like to get them into the ground as quickly as possible. If you must leave them out cover the roots with an old quilt or blanket and wet them down. They need to not dry out- they do not have rhizomes like irises. Far better to prep the new bed and even dig the holes before you dig up the plants.