There are 2 types of spark systems...
One kind sparks all four burners at the same time and is controlled by the spark switch on the burner valve itself. On this type, once the burner is lit you move the dial to the cooking position yourself. If one of the switches on the burners gets wet or sticks closed, it will spark continuously. This type of module will spark all four burnes at once, regardless of which knob is turned.
On the higher-end units, the module is much more sophisticated, looking for each spark to find a pathway to ground rather than manually turning it off via the knob setting. On this type of module (which yours has) each burner sparks independently and only the burner selected will spark, and then only until the module has sensed a flame. For yours to be behaving irregularly after so short a time could mean that you have a poor grounding system on the stove. Be sure you do not have this stove connected to a GFCI circuit, or the module will not behave correctly.
I suggest carrying a module with you in case it is not a grounding issue, since you are concerned about the distance, money, etc. In any case, it would be a good part to have for a spare as a precaution. Since most techs worth their salt already carry these on their trucks, field replacement becomes an easy choice for us.