Last thing I tried was some silver solder, which worked remarkably well while it lasted. Eventually it burned off and I was back to the bare metal, which ashed up and stopped triggering the flame sensor.
I tried adding a potentiometer in series with the flame sense resistor, and it made no difference. Added up to 10% to the sense resistor value, and it made no difference.
Now I've got a bit of stainless steel acting as a flame guard, forcing the pilot flame lower on the sensor rod. I cleaned off the sensor rod so it will be a while before it ashes up, but I'm running out of ideas.
It's not supercritical. I can clean off the rod and it works for a while. I'd just really like to have a solution that works once and for all.