For anyone coming to this old thread via a search: I haven't tried this, but it might be worth trying a compression washer. I'm not very hopeful, not on technical grounds but because if that worked, the manufacturers would surely do it; repeated heating and cooling are a sure-fire way to loosen things. There are several different types of compression washer (see Wikipedia Washer(hardware), section Spring and locking washers); I don't know which would be best.
If trying Loctite I wouldn't be worried about food-grade types, it's well out of the way of food (unless the screw is actually inside the pan, which I've never seen).