You raise an intriguing issue. I'm not sure, however, that your question is best framed in terms of 'ethical subjectivism'. This term can cover a number of views.
There are four formulations of ethical subjectivism which readily
come to mind. 1) A moral judgment is subjective if it cannot be made
and justified independently of the attitudes of some particular human being or groups of human beings. 2) A moral judgment is subjective if it merely describes the attitudes of the utterer and/or expresses these attitudes. 3) A moral judgment is subjective if it is
formed, skewed, or at least strongly influenced by an emotional bias
or prejudice of the person making the moral, judgment. A moral
judgment is subjective if, while it purports to refer to 'something out-
side the speaker's mind' all it really means (all the speaker has the
right to say, or all he can be warranted in saying) is that the speaker
approves of what is being done, advocated, prescribed, commended,
or generally approved of. (Kai Nielsen, 'Does Ethical Subjectivism Have a Coherent Form?', Philosophy and Phenomenological Research, Vol. 35, No. 1 (Sep., 1974), pp. 93-99: 93.)
This doesn't logically rule out the truth of at least some moral judgements but I think what you have in mind can best be discussed in terms just of divine omnipotence and moral realism. Shall we try that ?
DIVINE OMNIPOTENCE AND MORAL REALISM
A theist such as Descartes interprets divine omnipotence in very strong terms. For Descartes it means not merely that God can do anything which it is possible to do but that there is nothing, absolutely nothing, which is impossible for God. God can change the rules of logic and mathematics, abolish the laws of nature and, if God chose, alter the requirements of morality. God could make unnecessary suffering a good thing, justice a vice, love an abomination. You get the picture.
Descartes does not believe that any of this is to be expected from God. It is simply an acknowledgement of God's absolutely limitless power.
Now, on such a view of divine omnipotence, God could alter totally what you call the 'moral facts'. There could be moral truths, and moral realism be the correct ethical position, but this would be no restraint on God's replacing those facts completely and creating others - even quite contrary others. There would be new, different moral facts but they would still be moral facts and moral realism the correct ethical position.
On this approach, you don't need to hypothesise 'another God'. The present God could do all this. One extra point to note - a complication - is that you refer to 'immutable' moral facts. I'd just suggest that if they really are immutable then prima facie not even another God could change them. But on the Cartesian approach, since God is not bound even by logic, God could create moral facts which are immutable - and then change them. 'But it's contradictory to hold that the immutable, or unchangeable, could be changed'. Agreed, but the Cartesian God can alter the rules of logic so that it is not contradictory.
I think your basic intuition is sound. A God who/ which can change moral facts - a Cartesian God - could preserve moral realism. Moral facts would remain facts, or truths, but their content could change in the exercise of divine omnipotence. It's this changeability which I think you have in mind when you talk of 'ethical subjectivism'.
Cartesian omnipotence is very far from being the only possible or defensible form of omnipotence. But it is one conceptual possibility, and I have used it as such here.