See "The Catechism of the Catholic Church", page47, paragraph 153, entitled, Faith is a Grace.
While someone might make a reasonable case that "Grace Alone" is what the Catholic Church teaches, "Faith Alone" is most definitely not what the RCC teaches.
Faith comes through the Grace, is fostered in us by the Holy Spirit, and leads us to our Savior Jesus Christ. As we move closer to Christ and cooperate with the Holy Spirit, our faith deepens. Our cooperation with the Holy Spirit along with the additional Grace we receive through the Eucharist and other sacraments in turn increases our faith which draws us closer to Jesus Christ, in a cycle that draws us each as close to Christ as our cooperation with Grace will allow us to go, up to and including Sainthood for those with sufficient Faith and trust in Christ to totally surrender to Him.
So, like I said, someone could argue about whether or not "Grace Alone" is Catholic teaching but not "Faith Alone". Especially not "Faith Alone" as described by "sin boldly" Luther, those who deny the Trinity, those who defame The One, Holy, Catholic, and Apostolic Church Jesus Christ Himself established, and the vast majority of those who espouse Luther's "Faith Alone" heresy and it's close cousins derived from various Eastern cults rather than Scripture.
In all actuality, the majority of my own experience with teachings of faith, ended up on the same or much similar grounds as the way you here in this post describe the Catholic teachings (which I have seen explained before similarly).
The language employed can be a bit different. Remember, as I have previously stressed, the 5 Solas are meant to stand all together, inseparably. So in the end, the Reformed churches do not preach any of them singularly. I'm no Lutheran or Calvinist per se. But here I am defending them from the most spurious of the allegations and characterizations which you've casually tossed about, for reason that guilt of one or even dozens of preachers pushing watered-down "milk of the word" messages, do not equal all share in that same guilt.
More than a few, I would say the vast majority of those teachers or preachers I've been exposed to personally, teach nothing at all like the cartoonish characterizations resembling more televangelists than the Baptist church on the corner.
Where we part company is the belief that what is formally known as the RCC today, is the full embodiment of the Church which Christ established.
I was baptized in ocean waters, by a non-denominational Pentecostal leaning church, and received a baptism of the Holy Ghost right then and there. Until Vatican II, that much would be a doctrinal impossibility according to official RCC dogma.
I do not believe for one moment that such a baptism never transpired (with the same results, for others) before that above mentioned modification in official RCC doctrines took place. Then there is the issue of the many anathemas still in force, never formally revoked...
Oh, well. If I'm looking for perfection, there is only one direction to look. Up, of course.
Good luck on your journey.