The obvious theist counter-reply is that the structure of God's desires is logically related to the essence of God, in a way that you can't have the goodness without the God nor more than God without the goodness, they are part of the same logical structure. (Aquinas: "God is by essence goodness itself")

I think this is a self-consistent metaethics as metaethics goes. The problem is that God is at the same time part of the realm of abstract logical structures like "goodness", and a concrete being that causes the world to exist, causes miracles, has desires, etc. The fault is not in the metaethics, it is in the confused metaphysics that allows for a concrete being to "exist essentially" as part of its logical structure.

ETA: of course, you could say the metaethics is self-consistent but also false, because it locates "goodness" outside ourselves (our extrapolated desires) which is where it really is. But for the Thomist I am currently emulating, "our extrapolated desires" sound a lot like "our final cause, the perfection to which we tend by our essence" and God is the ultimate final cause. The problem is again the metaphysics (in this case, using final causes without realizing they are mind projecting fallacy), not the metaethics.