Then how can you know that...”One who is not Catholic cannot claim to know...”? If you are a Catholic, you know only Catholic experiences. I am arguing that the Bible does not support your claims of “deeper experiences” with God. Sorry, it’s not there. Until you are a Biblicist and not a Catholic, you cannot claim to know what is in the Bible.
You assume that Catholics don't know the Bible. For us, the Church has covered the translation and interpretation. But it also teaches that the Word of God which is the Bible is living, dynamic. Each day, when Salvation posts for us, we receive readings arranged over a three-year cycle that are read at Mass and on Good Friday (the only day there is no Mass). We're not taught by memorization, but by application. Over the years of my life, in several versions, I have read the Bible. I'm older now, and my syntax and recall are not what they used to be. But I still have it in my heart. And when I'm frightened, or upset, poor just need a verbal"hug" from a loving Father, I hold that Bible close to my heart, then read where He chooses to send me. Sometimes I choose my own, like Job 37, or the Psalms, poor the Last Discourse on John's Gospel. We do love the Bible, contrary to popular rumor. My Nanu (grandfather in Italian) read it out loud to my Nani who was illiterate but wise. My Mom was the youngest of -are you sitting down? 16. She got to hear, then did the same for me when I was little. She survived cancer when I was a baby, and prayer and God were part of our lives. Experiencing prayer? What of a 3 year old who, when in church with her parents prayed, "Now I lay me down to sleep..."- it was the only prayer I knew, but it came from the heart of an innocent child praying to God. I don't remember that in particular, but as I grew older, Jesus became my companion- I never saw or heard him, but I knew He was there. Not an imaginary friend, I had one of those, as most only children do- but Jesus. And I spoke to Him and knew He was with me then, too. I loved hearing the Scripture- and looked at the pictures in my Mother's Bible that she used to read to me from, and explain then read.
I hope I haven't been boring, sorry to go on so, but I grew up learning the meaning of Scripture- not much memorization- but how to live and why. Still learning. Hope I never stop. Even when I was away from the Church for awhile, I still read the Bible.
I pray that, if you haven't, you do experience the kind of prayer spoken of. It is a gift from God, and something to hold on to when life runs you down and you hit a bit of a bump on your prayer life.
God bless you, D! May you always stay close to Him, in good times and bad...