Caring for and pruning papyrus in a container

Last spring, I got some King Tut papyrus and put it in a big pot. It's beautiful, needs watering often. But I have no idea what I'm doing.

When the stalk died, I usually just cut it off at the base. The problem is, I now have a bunch of stumps, and the roots are getting huge enough to crack the pots. New stalks are skinny and not thick, because I think the stumps are constricting them.

What should I do for the next year to have nice big stalks? Repot them? Chop the roots up and replant it?