Got a respite from the rain, so went out to the heater to do some more experimentation. Hooked up the manometer to the input side of the gas valve, fired up the heater and ... it fired right up. So I took the opportunity to adjust the supply regulator to its stated output while the gas was flowing (8" wc) and did several more trials, all of which worked perfectly.
So I thought I better check the output of the gas valve to see if perhaps my adjustment on the input side had now taken it out of spec. The only changes I made were to put the cap on the supply regulator adjustor and move the manometer from the input to the output side of the gas valve. Of course, the heater no longer fired, going into type 2 failures (flame just enough for the controller to sense that the burners were lit, but then the flame goes out as soon as current is removed from the igniter).
From watching the manometer on the input side during the two failure modes, it appears the difference is that in failure mode 1, when the gas valve opens the pressure on the input side drops below 2" and its not enough to sustain any real flame; in failure mode 2 the input pressure is between 2" and 3", which appears to be enough for the igniter to partially light the burners so that a flame is sensed, but it's not enough to fully light the burner so when the igniter goes out so does the flame.
There is nothing but 1" hard pipe between the meter and the supply regulator, so I'm concluding that the supply regulator is flaky and needs to be changed out. While I'm having that done, the supply should be reworked to use hard pipe from the regulator to the gas valve, install a trap for debris/moisture, and install a union just before the gas valve so that if I need to pull the valve and manifold it will be much easier to do. Does this make sense or am I overlooking some other possibility?