Sure, I'll help with this experiment in any way I can!
The problem, I find with using the lower parts of the stem is that the older traps have so much prey in them, that if the detritus feeders (small snails, shrimp etc.) don't pull out those spent carcasses, they can get hit with filamentous algae. Otherwise, any healthy section of stems should produce new plants quite easily.
Glad to hear that you have a good crop of large monocot companion plants for them, you might notice that the healthiest strands of Aldrovanda are those that are actually tangled up with, and commingled with the exposed roots of these plants. Phragmites produces busts of roots just below the surface in areas that are a little deeper, and the Aldrovanda that find themselves anchored in these mats grow very vigorously. - Rich