In a lot of ways, this has become a semantical battle between Catholics and Protestants.
Protestants say "a man needs an engine to drive a car". That's a true statement.
Catholics say, "a man needs gasoline to drive a car". This is also true. The engine (faith) may be the instrument that moves the car, but fuel (works) is what makes the engine an engine in the first place.
What I'm saying is this: we cooperate with our faith. That faith, however, thrives as a result of our efforts to live as Christ - as Christians. If that faith does not thrive - if that faith is starved by a rejection of doing good works, then we cannot cooperate with God using that nominal faith. It's still faith given to us. But it becomes faith neglected by us, and therefore, renders us impotent as vessels of God.
I don't think you realize it, but just coming here and discussing Christ with us Catholics is a good work on your part. It will bolster your faith and lead you to truth. Not necessarily because you hear something specific from one of us, but because, as Christ said, "those who seek shall find, knock and the door will be opened to you".
Your goal (I assume) is to come closer to Christ and spread the Gospel. My friend, you are doing so! If you seek truth, you will find the truth.
" The engine (faith) may be the instrument that moves the car, but fuel (works) is what makes the engine an engine in the first place."
I truly appreciate your attempt to find mutually agreed upon middle ground (no sarcasm whatsoever). But your analogy falls short to the Protestant. A Protestant would agree that Faith is the engine, but Grace is the fuel, and our works are the emissions:) Unless by works as fuel, you refer to those of Christ.
God bless.