It was standard Roman practice to absorb deities the elite liked into the state cult. Don't really need evidence for something that was standard practice.
I did mention that Julian wanted to absorb Yahweh into the state cult.
That's not really the point I am making In the first and second centuries, the Romans tried to do this but the Christians resisted. They wouldn't budge because their faith taught it to be idolatrous. We have evidence from the anti-Christian polemicist Celsus that he even attempted to convince Christians to accept this but failed. The attempts were thus abandoned. Julian, revived this practice as you say with YHWH. However I see no evidence that Constantine ever tried to do this, not the least because he claimed to believe in One God and his Council of Nicea proclaimed, "We believe in One God". He made Christianity more emphatically dogmatic on its monotheism than it had ever been.
The practice was revived after him by Julian, as you say, in his attempt to return the Empire to its pre-Constantian mode and stop the growth of Christianity which had burgeoned under Constantine as a result of his example and not through state coercion, as Theodosius later did.
The only evidence we have from Constantine is that he believed himself to be a monotheist. He referred to God in the singular and publically voiced his personal abhorrence for pagan temple sacrifices of animals. Now, I see no political expedience behind why it would be necessary for him to promote equal tolerance of paganism yet describe its beliefs as superstitious error when this was the majority religion of his subjects, unless he genuinely believed this to be so. If he was still somewhat pagan, this makes utterly no sense to me, since Christianity was essentially very minor at this stage and widely hated by a public who had been fed anti-Christian propaganda under Diocletian. There were rumours in the first century AD under Nero that Christians participated in wild, incestuous orgies because they called each other "brother and sister", and practised cannibalism. The Emperor not only embraces this strange, mistrusted religion but defends its teachings before the public to the detriment of paganism. I ask you, why?
Constantine did not believe in forcing non-Christians to embrace Christianity because he believed, as Lactantius taught him, that religion was an arena for the freewill and could not be coerced. He therefore had no choice, on account of his belief in religious liberty and the pagan beliefs of his subjects, but to continue with the duties of the imperial cult in what was a pagan state. Constantine did not deviate from his belief in non-coercion in religious matters. His Church, was a different matter, he believed that as Christian Emperor he had the right to intervene in church affairs and promote his particular form of Christian orthodoxy. That was the golden exception to the rule. He took a vested interest in dynamics of the inner workings of the Church, which he did not have for paganism.
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