I don't think the literal biblical God requires, is required for, or created the morality we sense with our consciences (though I leave open the possibility that God, even a biblical God created our consciences). By your definitions that would make me someone who subscribes to "objective morality", but I don't believe it is necessarily objective either (though it could be).
We have consciences, whatever combination of nature or nurture imbues this in us. I see this as a faculty, like our reason or vision. I believe we use these faculties to judge morality. We can makes mistakes, we can do things that go against our consciences. But using our consciences is not the same as "doing whatever we feel like".
We also know that vengeance, and selfishness would not be seen as good by many who make use of conscience (Evil, in fact, by many people of conscience).
I heard a good question a while back: "Why do piranhas not eat each other during a feeding frenzy?" What moral code are they following? What makes wild, seemingly ferocious, animals take care of their young, and cooperate to find food? Are they referring to a holy book or authority to be able to do this?