Have you tried using hay or dried grass in the nests?That is good to know, because I can make heavy cardboard shreds for free, but I have to buy my pine shavings. Advantage in cost to the free heavy cardboard shreds.
Pine shavings have a nice smell to them, whereas heavy cardboard has no smell. Pine shavings are also softer in the nests than heavy cardboard shreds. I don't know if that makes a difference to you or the chickens, if so, advantage to the pine shavings in those cases.
It seems to me that hens prefer long strands of dry grass-type material for nests, when they have them. So if any part of your property grows tall grass, maybe try cutting some of it after it dies & dries out for the winter (alternately, cut it in the summer and dry for hay, but this is not the right season to try that.)
I would not bother buying hay or straw for nest bedding, just suggesting that if you have an easy free source you might give it a try.