If the First Cause could have logically been different, then the first cause would not be logically necessary, and it could not be the real first cause. Remember our main example of logical necessity - mathematics. It makes no sense to say the laws of mathematics might be different. It could never be true that 1+1 = 3, no matter what possible universe you are in. If there were 1 billion universes, the laws of mathematics would apply to all of them. So mathematics is logically necessary. It is true throughout the entire omniverse, always, no matter what.
Another issue with the laws of physics being the First Cause is that there are many of them. I composed a proof earlier why the First Cause has to be singular - do you disagree with that proof?
Finally, the laws of physics aren't actual things. They do not exist in and of themselves (which is necessary for a first cause) - they only exist insofar as spacetime exists - these laws only exist insofar as things exist which happen to obey them. If this universe did not exist (if timespace and all that is in it did not exist) then these laws could not exist. The existence of the laws of physics is entirely dependent on the existence of this universe. The existence of any set of physics laws is entirely dependent on the existence of the universe that they govern.
The First Cause must be the thing on which the existence of everything else depends. It cannot depend on anything other than itself for its existence, for everything else must depend on it for their existence. The laws of physics cannot possibly satisfy this.
I agree that it is logically necessary that some set of physics laws exist - if a universe exists. For every possible universe, their must be a set of physics laws to go with it. But this only proves that the laws of physics are dependent on the existence of a universe. Without a universe, no laws of physics can exist in the omniverse alone. They are therefore inherently not logically necessary in and of themselves.
This test does not seem to be favorable to God . . . yet. But as we slowly learn more about the First Cause and rule out other possibilities, I believe we will see the logically necessary First Cause continue to show the attributes which we ascribe to the God of Christianity. So far, again, we know the First Cause must be transcendent, necessary, eternal, uncaused, immutable, self-existing, and independent. Now, I'm arguing that it makes the most sense for the First Cause to have a mind.
You said "Simplicity and indivisibility are not synonymous with each other." When I have been saying "simple" I have thought "indivisible" or "not composed of any parts". So this may have been the source of a misunderstanding - how do you define simplicity and complexity?
The indivisiblity of a mind matches the indivisibility of the First Cause, which makes it likely that the First Cause has a mind - this is the logic that I propose as evidence that a mind can exist without a brain.
I argue that annihilation or eternal slumber would indeed "confirm the man forever in his present happiness". For, having lived a full and enjoyable life, and probably not expecting any kind of afterlife anyway, his conscious is either destroyed or put to sleep - he is at peace, with not a care in the world. He takes this as confirmation that he found the best way of life by hurting others.
Do you define Justice differently then I do? I would say that Justice means that when someone does something wrong, they really do deserve punishment. Punishment is not only corrective under Justice - it is necessary. The balance must be made equal - thus Justice is symbolized as a set of equally balanced scales.
God is Truth. If someone seeks the truth, they will find God.
“For everyone who asks, receives; and the one who seeks, finds; and to the one who knocks, the door will be opened.”
Matthew 7:8 NABRE
If someone is indeed honestly mistaken - if they seek the Truth honestly and earnestly, and reach the wrong conclusion by no fault of their own, God will not condemn them. In seeking the Truth, they have sought God without knowing it. God does not condemn us for our imperfections - such are human nature. Only our sins.
The system cannot be "gamed". If the wicked man enjoyed a lifetime of wickedness with the intent to repent on his deathbed and get "the best of both worlds" his repentance would probably not be genuine. Or a tempting thought might come to him as he faded away, and his habituation to give in to evil would be his undoing.
If, on the other hand, his repentance was truly genuine, then justice is still served - for Christ took on the punishment that he deserved. In His love for us, Jesus took upon Himself the punishments we all deserved in His Passion. And if the Lord wishes to give this man eternal life as well as one who has served the Lord all their lives, what grounds do we have to argue? Are we envious because the Lord is generous? The one who has served the Lord all his life will still recieve his fair wages.
(See Matthew 20: 1-16)
If the crisis of faith of the man from your example, after serving the Lord His entire life, is genuine - if he truly believes that atheism is the Truth, and is not rationalizing or telling himself that because it is comforting, he will not be condemned. I do not know if your example is possible, as I have no experience in this matter. But God is Just.