Thanks for the suggestion, Phil. I tried it and didn't get any different results. Eventually, it got to a point where it would work with the original cable. What I needed to do was set the switch under the pedal to "Other" (from "Standard"), and power down the Helix and let it power back on with the pedal in that state. Then it worked (of course, backwards, just like everybody else's 3rd-party expression pedals have been reported to do). So I'm in business now. Thanks for the assist!
chromecity's post in External Expression pedal - doesn't seem to be recognized was marked as the answer