CA:
The dilemma described in the OP doesn’t hit me quite that way. In my mind, the Torah is the absolute truth. There can be no other system.
Imagine we had a world where the Torah did not exist (obviously not reality). It would be incumbent upon us to establish a moral code, since without one, the world would quickly deteriorate into chaos. However, the inherent bias we have to ourselves would guide us and influence us to create a code that was somehow pleasurable to us. The restrictions we know of would never emerge from a code that is based only on our own thinking.
So the basics of morality must emanate from a spiritual source. What follows is that there can be no true conflict between Torah and morality. What I need to take from this is that anything that is moral has its root in Torah somewhere. Hillel derived a general rule from Torah. He proceeded to instruct the individual to pursue the details and related values through Torah study.