short of a servo moving with a conductive pad attached to it simulating a finger press im not sure what else to suggest 
Perhaps pairing up with someone which is more comfortable in hacking into the stoves wiring. Keep in mind that a touch pad button wouldnt have any significant voltage flowing through it and it would merely trigger a transistors for example. some careful diagnostics would need to be made by an electronic engineer for the correct way of bypassing it, though it would be alot more practical and neater than robotic fingers so to speak 