Here's some info I found:
"Balloon
flowers should not be transplanted once they are established. Division may be done in
spring but the roots are thick and division must be done carefully as they are difficult to divide. Set the crown one inch below the soil surface. Propagating by cuttings of non-flowering shoots in summer may be done by rooting stem tip cuttings under mist. Otherwise they are best propagated from
seed sown in the
spring or by setting out young container-grown
plants in
spring or fall, spacing root clumps 12 inches apart. The
seed germinates in 2 to 3 weeks at temperatures between 65 and 75 degrees and is the preferred method of propagation. Light is necessary for
seed germination."
It sounds like it would be better to grow more from
seed rather than risk trying to divide it. I have several Balloon
flowers myself, one of which I've had in my garden for about 6 years.