As a summary, that's fine.
" If the BTK had free will to do otherwise, then God must not know what he will do.
Whaaaat? BTK has a Free will. God's knowledge of what choices he'll make and actions he'll take are independent of BTK's Free will. Where do you get the, "God must not know" from the fact BTK has a Free will? The conclusion is illogical.
" Therefore, either God knows and there is no free will OR God does not know.
The use of "therefore" is irrational, because it follows from and illogical construction. The only way BTK could not have Free will is if God interfered with BTK's sovereignty over his own will.
Perhaps you missed the fact that God foretold of His betrayal at the last supper and before that. God did not interfere with anyone's sovereignty of will, even to His own mortal end. He said to Pilate to whom the betrayer and the "priests" handed Him over in John 19:10-11
"Do you refuse to speak to me?" Pilate said. "Don't you realize I have power either to free you or to crucify you?"
Jesus answered, "You would have no power over me if it were not given to you from above. Therefore the one who handed me over to you is guilty of a greater sin."
The power given from above is the gift of life and sovereignty of will-Free will. Pilate's choices were made in relative ignorance. The betrayer's was not. That is why his sin is the greater sin. Pilate's was just to kill to end a bothersome conflict.
He came to teach. Learning and judgement requires the effort of Free will.
No. God had programmed BTK's existence, just as he has programmed yours.