Often synagogues use non-jewish people to operate lights and air conditioners on Shabbat. Whether fire and electricity are the same is another issue though so if they are different, the case of using a shabbat goy does not apply.
My big question is whether a Jew really has to be involved for the food to be kosher. If a non-jew was able to perform the role of a mashgiach to the extent of how the torah commands the food to be prepared, could that possibly suffice? The biblical laws could all be followed by someone of another religion, but could all of the rabbinical ones be followed? If not, which ones.