You don't need to move them. If you leave the shoots to grow on, it will turn into a multi-trunked. You can cut off the dead original trunk if you haven't already done so.

you were lucky, I lost my cordyline in the bad weather too, but it just rotted at the base and never came back. It was a present from the Mothering law as well, but she was very good about it and bought me another plant an acer which I prefer any way. sorry I know this is not answering your question.