We adhere to the Church Fathers. They have not left the teachings of the Apostles. You gave two quotes, St J. Chrysostom where he uses the phrase "faith alone". St Basil however, puts the correct wording of what faith alone actually means, that is "faith alone in Christ".
The Church has always adhered to the justification by faith.
The Church in the last 500 years does not use the alone any longer when using faith because it does not mean what the protestants have made it to mean. It is neither a simple faith, nor a faith alone. It is the protestants who have left the fold of the fathers and have isolated its meaning to a simple faith, a one-time event in the life of the believer, which it is not.
Therein we have always denied the protestant understanding of 'faith alone" as did and do the Roman Catholics.
You will never find "faith alone" ever written in the Bible except in the negative in James 2:24.
However, the only way to correctly phrase it is as in Rom 5:1 , Rom 1:17, Gal 3:11, Eph 2:8 and many more.