Well, just having a single incandescent bulb in place stopped the flickering, so it appears that Brian's idea was on the right track. I replaced that incandescent with another GU10 LED, this one is dimmable, and it has also stopped all the flickering.
The logic behind this just seems a little bizarre.
1. LED lights in place -> Make sure you get a switch that works with LED
2. Get switch that works with LED -> Make sure that the LED is dimmable
3. Get LED that is dimmable -> Now it works great with a non-dimming switch!
If I had any inkling that the WS13A might not work with these switches then I would likely have acquired a different switch type from the start, because it appears that the bulbs I had just won't be working with an X10 switch of any kind. It isn't like I absolutely need dimming, but if I have to get new LEDs to use LED at all... oh well, I'm glad to have it working properly finally, now to get the rest of the house X10'd.