I will address your point first, and then restate my question since they are still separate, I think.
First, I completely agree with you that not all are "invited to salvation" if by that you mean elected. But the Gospel is meant for all men regardless (the great commission did not distinguish to go only to the elect with the Gospel), which gives all men even less an excuse for their neglect (if they do neglect the Gospel) - but indeed the actual turning to Jesus & faith must be, as you say, given to them by God Himself. Jesus in John's Gospel makes that quite clear when he said no man can come to him except the Father draw him (John 6:44). So there we agree. I also agree with total depravity, man is unable to help himself, though he is still responsible (Romans 9:19-22).
My question has to do with whether the assumption that Jesus' atonement and salvation are the same is valid. Certainly they are related, but I draw a certain line of distinction. The atonement was made apart from any man receiving it because it was affected at the very moment of Jesus' crucifixion (and even regarded as being done from the foundation of the world - Rev. 13:8). As such the atonement was given for all men (not to all men - mind you - it must be received also), while those who are actually to receive it are only determined/appointed as such according to God's election.
I gave the example of how the High Priest yearly gave atonement for all of Israel, but that not all were saved (the opposite being 'destroyed' - as Korah was). The atonement is useless to us unless it is received & applied, but it was for us nonetheless, whether we receive it or not. The bronze serpent was made by Moses to save the people from the serpents' bite, but only those who looked upon it were saved. All had equal opportunity. You however may frame the incident in terms of "those who neglected the opportunity were were not elected to be saved/live". But it doesn't change the fact of the opportunity. That is why man is still without excuse. I think those two Old Testament examples bear out my point of how atonement can be for all people, while not all will be saved.
1) True.
2) True.
3) True.
4) True.
5) True.
Once again, John 6:44 confirms what you say here.
I'm actually addressing atonement here, something different from what you mention in your OP. It's a somewhat broader subject (perhaps for another thread). I just want to make sure that there is no confusion on that.