You are quoting secondary sources again. On what basis does Locke say the ante-Nicene Fathers were Arians? No answer, it's just his opinion with any substancial argument.
Have you read Justin's any writing? Btw. which Apology? First or Second? Justin is arguing that Jesus was fully God!
Yeah, I know this JW argument, that angels and judeges were also called "gods" in the Bible, so the Son can also be "god" in that sense. This argument suffers from the common issue of analyzing the word God ("god") instead of what it signifies. Because neither angels, nor judges, nor even Moses were God in the same sense as the Son. He truly created the world, was present from the beginning, and without Him, nothing came to be; He was in the form of God, etc. When we combine these, we still get a higher concept of divinity than what is applied to people or angels in Psalm 82 or other places.
Jesus did not apply Psalm 82 to Himself but to beings of lower dignity to whom the word of God was addressed. Judges, or perhaps angels. And He immediately added: If it was allowed to be said about them, how much more about me?
I can easily show that Jesus' divinity is greater than theirs (i.e., they are not only begotten gods, alphas and omegas, creators, etc.), but all you can bring up to support your claim is that Jesus received His divinity from the Father (through His birth). So, you arbitrarily claim that Jesus is in a category below the Father regarding divinity based on the mentioned "below the Father" category. You only tried to prove the existence of such a category, but you couldn't deal with the fact that Jesus doesn't fit into it. For example in terms of dignity, He is immediately equal to Him (Jn 5:23), and for now, this is enough for the sake of proof.
The fact that the Father is the source of divinity and that He begot the Son along with His divinity. Therefore, if in the relationship between the Father and the Son, God specifically refers to the Father, it is because the Son did not give His divinity to the Father but vice versa.
I recommend that you read the New Testament coherently from the perspective of how many times the indefinite "theos" also means "the God." Such is Phil 2:13 or 2 Cor 1:21. Indeed, one cannot infer a lower degree of divinity from the absence of the article.
Thomas' exclamation was indeed an address, but a singular address usually refers to a specific person, which in itself replaces the definiteness that might be missing from the address and is not always indicated there. But regarding the essence, Thomas called Jesus not "a god" but his own God, even though both of them knew the commandment: You shall have no other gods. And Jesus approved of this use of words by Thomas at John 20:28. As for the source you quoted, it claims that this is a similar ranking formulation as the speech to the judges in Psalm 82; it is merely a desperate effort to impose an analogous use of words on Jesus' divinity elsewhere (which is of much higher rank than the judges).