To elaborate on my reasoning, in failure mode 1 (flame on only momentarily, less than a second), it's clear the controller is classifying this as a failed trial and goes into IF after 3 attempts. In the case, flame is not being sensed, but it's not going out because the valve got closed; it just never lit in any meaningful sense in the first place.
In failure mode 2 (flame on for about 2 seconds), it's clear that the controller is NOT classifying this as a failed trial (because it does not go into IF after 3 attempts; it takes 10 attempts before it goes into IF). In this case, the controller IS sensing the flame. I believe it goes out because when a flame is sensed, the controller pulls the plug on the igniter (as stated in the manual). But the burners have not really been fully lit at this point and they go out when the igniter ceases to glow. If the controller left the igniter on for the full 4 seconds, my guess is it would probably light, but I have no way to know for sure. That's my theory anyway.
It's also clear that my gas supply has some issues (detailed in another thread). So I'm leaning towards this as the root cause of my problems.