The argument that a conscious god is the source of objective morality falls flat at face value. If it is truly objective, then it cannot be contingent upon a mind, it would necessarily be subjective to that mind.
For objective morality to exist, it must exist independent of everything, like the laws of logic.
Furthermore, any theist that wants to argue about the existence of objective morality is setting themselves up for failure, because at that point, any action their god makes or has made in the past is comparable to any action a human may take.
For example, in the world of moral objectivism, if it is moral for YHWH to kill an innocent to pay for the crimes of another person, then it is also moral for a human to do the same. If it is moral for YHWH to cause the deaths of children for being bullies, then it is moral for humans to do the same. And so forth.
Effectively, there is no such thing as moral objectivism in theism. Not when there are one set of rules for a god and a different set of rules for humans.