I would be in the camp suggesting a warm hairdryer while it is hanging. As said a roll tube from a carpet will be perfect for rolling and storing it. They come in different sizes, so you should hopefully be able to find one that is around 4" in diameter to roll it on, and then a larger one to slide it all into for protection while storing it. Find a small shop, that sells cut lengths direct to the customer. They will probably be more than happy for to take what you need. After all they are probably paying through the nose for disposal of them. I know here in the UK the manufacturers will sometimes pick the old tubes up when they do a delivery, it's part of our laws on recycling, so you may need to go just before a delivery is due. Just storing the things can be a problem for a lot of places. A friend of mine has a carpet shop.
Alan