There is one more detail that just came back to me.
When I was removing the old dimmer, I am pretty certain that the three wires (red, black and uninsulated) were wired to the three terminals on the switch (C, L1, L2 - it was a 2-way switch used as 1-way).
This is not a setup I've encountered before. Have you seen a setup like this? Is it even standard?
In retrospect, I should have noticed the unfamiliar wiring, and at least noted it down...
Alexei