One rule of thumb in bible interpretation is the "first mention" rule, whenever a term or phrase appears the first time, the same definition, connotation and implication thereof apply to all the subsequent mentions in the rest of the bible. "Sons of God" in Gen 6:3 literally means "godly or heavenly beings". "Son" should not be understood as biological male offspring, but rather the embodiment of a concept, such as "sons of chaos", "sons of thunder", "sons of the republic". Jesus frequently addressed himself as the "son of man", the emphasis was on his humanity, that even though he is the unique son of God, he manifested himself in form of a man, a humble carpenter from Nazerath. So whether you think these sons of God are angels or not, they are most definitely not mortal men. The whole purpose of using the term "sons of God" is to distinguish them from mortal men.
Or, the whole purpose is to distinguish between a godly line of people and an ungodly one. It seems to foreshadow what happens during the conquest of Canaan. Jesus uses "sons of God" of humans:
Mat 5:9 “Blessed are the peacemakers, for they shall be called sons of God.
Luk 20:36 for they cannot die anymore, because they are equal to angels and are sons of God, being sons of the resurrection.
Luke says that Adam was "the son of God":
Luk 3:38 the son of Enos, the son of Seth, the son of Adam, the son of God.
Couldn't there be a godly line there, such as that of Seth?
Jesus also uses "gods" of humans:
Joh 10:34 Jesus answered them, “Is it not written in your Law, ‘I said, you are gods’?
Joh 10:35 If he called them gods to whom the word of God came—and Scripture cannot be broken—
That comes from Psalm 82:1. Those are humans who are God's representatives, his judges that judge the people.
(All ESV.)
Also, you said, '"Sons of God" in Gen 6:3 literally means "godly or heavenly beings"." So, even according to that statement alone you cannot claim "they are most definitely not mortal men." If it can mean a "godly being," then it can mean a "godly human." As I have given above, there is reasonable to believe that that is the case.
Further, you are giving angels the ability to create for themselves, out of nothing, not only the appropriate male anatomy, but also compatible DNA by which they could procreate. That is going way beyond any biblical text and is purely speculation. We should stick with Scripture.