You may have some success with rhizome chunks, but it's not the best way. Depending on the species, I've had success rates of anywhere from 0-50% with propagating from rhizome cuttings, For the rhizome chunks that you are successful with, you still have the problem that the root mass is so small that you will only have small culms for several years. If you want to propagate larger plants and have close to 100% success you need to do field divisions, which means excavating out a root ball the size of a soccer ball or larger, with at least one culm attached. To do this properly is a fair amount of work. If you want more detailed info, email me and I'll send you something I wrote up a couple of years ago on this subject.

I place young plants in a nursery area where they're easily tended, after 2 seasons I dig them and place them out where I want them for screening. In the course of digging them up I find runners about 6 ft long that I dig up and divide into 18" sections and plant in shallow trench and cover with compost and water regularly. I get better than 90% that shoot and become new plants and the cycle repeats. Good luck.