If God does not ground morality then there is something outside himself that determines how he behaves, but then God is not a maximally great being and thus does not exist. God does not exist because all theistic accounts of morality fail.
I would say a moral argument against God could also be something formal like:
1. If God exists, he must be the standard of morality
2. But God cannot be the standard of morality
3. Therefore, God cannot exist
Yeah, that's something Craig seems committed to (I'm pretty sure he has argued for (1) because he thinks being the standard of morality is a great-making property).
Right. Craig himself and most theists are already committed to premise 1. A version of the Euthyphro dilemma would be the evidence for premise 2. Or it can be argued that God cannot or is not plausibly the standard of morality by other reasons. There are many ontologies of morality, why would God occupy a special place? What makes God so special or plausible?
Theists offer some reasons, but I don't find them convincing. It's not a simple 50/50 on whether God is the standard of morality. On the contrary, given the various metaphysical groundings for morality, the prior probability that God is the grounding is not very high; thus, the evidence, the posterior probability must be pretty high, but the evidence doesn't seem to be very high. Therefore, we have at least prima facie reason to doubt that God is the grounding and that he isn't in fact the grounding because of the prior probability