My argument allows both Halacha and morality to retain autonomy. Halacha is completely autonomous because morality need not influence its dictates (at least not directly), except in the rare situation where Halacha requires an action that undermines its very authority. Morality is autonomous insofar as it demands adherence to Halacha and has its own authority when Halacha is silent. This conception of the working relationship between the two allows them to retain their own conceptual space.
Another possible view of the relationship is offered by Kant. Kant believed in an independent morality that was synonymous with reason. He believed that morality can be used as a tool to determine whether Divine commands come from a just and good G-d. He states,
"If God should really speak to man, man could still never know that it was God speaking. It is quite impossible for man to apprehend the infinite by his senses, distinguish it from sensible beings, and recognize it as such. But in some cases man can be sure the voice he hears is not God’s. For if the voice commands him to do something contrary to moral law, then no matter how majestic the apparition may be, and no matter how it may seem to surpass the whole of nature, he must consider it an illusion."
Kant's problem is that man has no reliable way of ascertaining whether the command comes from a good G-d or an evil G-d. How do we know that it is G-d telling us to do an act and not Moloch, who requested that mankind sacrifice their children? For Kant the answer is that a command from a just G-d would comport with reason. Any command that is immoral cannot be the directive of a good G-d and must be ignored.
Kant's use of morality in this case is epistemic. We know that it is G-d making the command by the fact that the command is moral. My view of the interaction between morality and Halacha is that morality serves as a normative basis. The practical difference between the two conceptions is that Kant requires that immoral commands be rejected, while I would at least accept the possibility that Halacha can demand immoral acts. Kant clearly considers morality to be the primary system; I view the two on equal grounds, with Halacha having primacy because we have a moral obligation to abide by G-d's commands (I am assuming such a reason exists, but I haven't offered one here).
So the difference is how to approach the content of Halacha. Halacha is not necessarily influenced by morality in my view (besides for a few situations), while Kant would allow morality to dictate the actual content of Divine commands by asking us to reject commands that are not consonant with morality.