Responsibility and voluntary choice are not the same thing as free will. We affirm that man is indeed responsible for the choices he makes, yet we deny that the Bible teaches that man has a free will since it is no where taught in the pages of Scripture.
If faith through free choice is not a possibility, then why did Paul preach it? This is what Paul and the apostles preached (1 Cor. 15:3b-5):
"Christ died for our sins according to the Scriptures, he was buried, he was raised on the third day according to the Scriptures, and he appeared to Cephas, and then to the Twelve."
v.11
"Whether, then, it was I or they (the apostles),
this is what we preach and this what you believed."
Do you preach this? In Galatians 1 Paul warns about the preaching of different gospels. He even curses those who do so.
Why would Paul cite Deuteronomy 30:11-14 regarding faith?
"Now what I am commanding you today is not too difficult for you or beyond your reach. It is not up in heaven, so that you have to ask, “Who will ascend into heaven to get it and proclaim it to us so we may obey it?” Nor is it beyond the sea, so that you have to ask, “Who will cross the sea to get it and proclaim it to us so we may obey it?” No, the word is very near you; it is in your mouth and in your heart so you may obey it."
Paul says that faith IS possible - that it is not out man's reach and up in heaven so that man has to ascend beyond his capability. You seem to be suggesting otherwise.
The Bible teaches, rather, that God ordains all things that come to pass (Eph 1:11) and it also teaches that man is culpable for his choices (Ezek 18:20, Matt 12:37, John 9:41).
Yes, God is sovereign and we are responsible.
I believe that the predestination of Ephesians 1 is with regard to God's provision of Christ and the spiritual blessings that come for those in Him.