Illusive morals? I think the confusion arises because morality is in it's nature both objective and subjective. As you say, mores are not whims of the moment; they persist in the face of an individual's belief or disavowal of them, in the same manner that a teapot does. Mores may be studied and classified, and books are written about them which can be said to be accurate, or not. And yet, moralities are subjective, in that it has no reality outside of the minds of the societies which formulate them.
The situation is analogous to the valuation placed on money, or gold. That money is valuable is a real, objective fact of the world; it makes the difference between someone wielding enormous power vs. a stack of worthless paper. And yet, there is nothing objective in the world which confers on money it's value, outside of the collective agreement of the individuals who use it.
Maybe a new term is called for. Morality is neither objective nor subjective, but rather collective.