(Possible) Solutions

If several morals are in conflict, the one that is best according to one's own set of values should be picked. (This assumes that there exists a justified demand for a certain amount of moral self reflection)
Extend the criteria to include progressive morals (and accept tragical situations)
Atavisms are better countered by education than by moral protest (A good point for the two tiered approach)

If several morals are in conflict, the one that is best according to one's own set of values should be picked. (This assumes that there exists a justified demand for a certain amount of moral self reflection)