Solution to constant sparking
I hit the same problem after a new ignitor was installed. The burners would light but the ignitors would keep sparking. The one clue was that if all the burners were lit then the sparking would stop.
The problem was that the burners were miswired to the ignitor. The electrical connections from the ignitor to the control knobs are labeled 1 to 4. The electrical connections from the ignitor to the burners are labeled 1 to 4. If these don't match then things don't work. That is, if the knob that controls the front-left burner is attached to terminal one, then the front-left burner had better be attached to terminal one.
The reason is simple. When you turn on the gas the ignitor sends sparks to all four burners, for safety reasons. But it also monitors to see if the *specified* burner is lit. Once it detects heat, it stops sparking. If it's monitoring the wrong burner then it won't detect heat. It was an easy fix once we figured this out.
After this we still had one burner that when lit wouldn't stop the sparking. That's because its wire was loose, so that's another possible cause. It's odd that it's wire had a good enough connection to drive the spark, but not a good enough connection to detect ignition.