Thanks again for all your comments everybody.
Jean, the plant had got up to a few dozen growths by last year when I chopped it up to sell bits. I have 3 pieces now. Two of them have just 3 mature growths each, with a few new growths about 8" tall. One of them has just a single growth (cane); but, even it's got 2 nice new growths coming up. All 3 pieces got themselves nicely established and all 3 are in blooming mode now. In fact, the single growth division happens to be the one that had a flower open when I was in the greenhouse with the camera. That flower in the photo is number 4 from the tip of the stem. I'm not worried about the plant. It's got plenty of beautiful, thick, actively growing roots as well as the 2 new growths. Yes, if I could afford to just stop making divisions, this species does grow into a VERY large plant over time!