There is nothing in John 1:12-13 that negates a foreknowledge/omnipotence based predestination.
That gets to the heart of my and Marlowe’s objection that you can’t speak to God’s methodology of predestining, since you claim that it’s secret.
On the contrary. The fundamental argument of foreknowledge/omnipotence based predestination is simply to reinforce the free will of man to choose salvation. John 1:12-13 states that salvation is not by the will of the flesh or the will of man but of God. There are plenty of other verses that supports this including John 6:44. In fact, John will make no sense unless one suspense their understanding of free will.
Now it is very difficult, although some have tried, to make an argument that God looks down some time tunnel and see who is going to be saved and predestines them upon this foreknowledge. This argument has one deep flaw (many actually); it forgets (or doesn't mention) that God did this all before we were even created. So if we were to make a choice, how could God possibly have predestined us before the choice was made? How could He have "chose" us when He wouldn't have known?
That gets to the heart of my and Marlowes objection that you cant speak to Gods methodology of predestining, since you claim that its secret.
Tell me, why did God choose Abraham and not his brother to talk to? Why did God talk to Moses and not to Aaron? Why did Jesus call some to be in His immediate circle and others He simply told to go and preach the gospel? Who knows? This is all part of the secret counsel of God. And it isn't some great flaw in the doctrine's logic to simply say we don't know why God spoke to Moses and not Aaron.
It is a bit unseemly for people to criticize Reformers for saying "We have all the answers" and then when we say, "Well, why God elects some and not others is a mystery." we get a big, "AH HA!!!"
There is no greater EXAMPLE in scripture of God CHOOSING a people then the people of Israel. And yet we hear everyone can choose God. Well tell that to a Canaanite if you can find one.