How to cook whitebait without overcooking?
So, I am not sure whether this is a satisfactory answer as it suggests a different cooking method but here goes

In Greece whitebait (mostly anchovies) is either flash fried after being coated in strong flour or cooked low in the oven covered in lemon, oregano and oil. This latter method matches yours closely - essentially you want to confit it in olive oil in less than 100˚C and make sure you add plenty of oregano or thyme and - if you don't like the sourness of lemon (I do!) use lemon rind. If olive oil isn't plentiful where you are, you can get away with using sunflower oil although the result won't be as tasty. The cooking time is forgiving as it is really low heat.

In any case, the rule of thumb in Greece is to never boil small fish: either fry or oven cook.