I'm not objecting, just supposing or thinking outloud. As I said, I believe you are correct that Seth's line is the one that counted. Or in other words there is a Godly line that are born with an ungodly line. But it is only those that are of God that God counts. Or, in other words, the others don't count. In tracing Christ's genealogy in (Luke) we are told Adam was a son of God or 'of God'. (3:38) Note in (Gen. 4:16-24) concerning Cains line, that God doesn't even give the years that they lived.
So, when God told Adam and Eve to replenish the earth while in their sinless state, I believe He had only those of Him in mind, such as Abel, Seth, etc. Just as Adam was a son of God, or of God, so would these be of God. And, though the fall has now occurred, I think this is still the case. But, in some way another seed was introduced at the fall that produces a race not of God, from birth.
Did not Christ say, "He that is of God heareth God's words: ye therefore hear them not, because ye are not of God." (Jn. 47) And also, "Ye are of your father the devil, and the lusts of your father ye will do...." (Jn. 8:44)
Some like to say we who are believers now used to be children of the devil. I don't believe that at all. We were never children of the devil. Children of wrath in a fallen state, yes. But never children of the devil. We were always 'of God'. Always in the count. Lost and going to be saved.
Now, that may bring up another interesting point. Who are lost? If what I have said is true, then the lost are only those in the count. The very idea of lost infers previous ownership. This would mean those of the other line, not of God, of Satan, are not lost as they were never God's in the first place. They are at home in this world. The lost are those of God.
Stranger, your OP is over my head, but I would like to share a few thoughts. As you said, "I'm not objecting, just supposing or thinking outloud." I am doing the same. I am not saying it is right or wrong or even adds clarity to your topic. It is just something to consider:
Matthew 13 says, "Another parable put he forth unto them, saying, The kingdom of heaven is likened unto a man which sowed good seed in his field: But while men slept, his enemy came and sowed tares among the wheat, and went his way.
But when the blade was sprung up, and brought forth fruit, then appeared the tares also.
So the servants of the householder came and said unto him, Sir, didst not thou sow good seed in thy field? from whence then hath it tares?
He said unto them, An enemy hath done this. The servants said unto him, Wilt thou then that we go and gather them up?
But he said, Nay; lest while ye gather up the tares, ye root up also the wheat with them.
Let both grow together until the harvest: and in the time of harvest I will say to the reapers, Gather ye together first the tares, and bind them in bundles to burn them: but gather the wheat into my barn."
We know, just like the compassion of a net cast that draws in fish of all sorts, some baking in the hot sun; fish does not always mean fish, but rather means men. So, a man sowed good seed in his field. Then the enemy came and sowed tares among the wheat. Something to consider, the tares are sown within
his field ( kingdom) growing amongst the wheat.
(Genesis 3:15) "And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel." Satan has a line of corruptible seed, correct?
(Paraphrasing) They asked, "do we go and collect those that are yours(the wheat) now?" "No. Let the tares and wheat grow up together." The Pharisees were told by Jesus that Satan was their father. Were they not tares sown among the wheat?