A bit of bad advice from someone that went through something like this.
Give it up, continue to be friends if you like, but it is not likely she sees you as the "alpha male" desirable to her. I hate that term that someone used on another thread. But there is some truth about it. Women seem to double talk sometimes. Like men that hold out for the perfectly groomed, "hot" babe, women do something similar. Your best bet would be to let her go in that way. For both of your sake limit your contact. These bonds only lead to greater heart ache. And as the kind of male you want the "idea" Catholic woman as your bride. But not everything is as it seems.
I was crazy about a girl in a similar relationship. Her father was a deacon and her mom the Director of Liturgy and Music (choir leader really) They looked like the perfect catholic family. She put me up on a shelf convenient at her beck and call. Ultimately she blew me off and I realized she was playing me all those years growing up. She flirted and did all those girl things that attract men... those subtle indicators to lure her mates. I was a fool and fell for it. Ultimately I went to the seminary. I returned and met another girl, her high school competition coincidentally. I found out from her that the girl I had the crush on was like that and did that to a lot of other guys. She had a reputation for being a "tease". (my wife just walked in smiling or rather laughing at me for being up so late - I'm ripping CDs for her iPhone). After wasting another 4 years with the competition that dumped me for another guy she ultimate married I realized that I was looking in all the wrong places. I joined the military, moved across the planet and made an oath not to date while in the Army, for my own good. I gave myself to God first and if He wanted me to marry he would present a practicing Catholic woman for me. Until then I committed to return to the seminary to serve him believing that he wanted me to give myself to Him first and foremost. So I did.
Ironically, the girl of my dreams turned out to be someone I never suspected, a stranger, a non-Catholic, but a sweet Protestant woman, 4 years younger that the other 2 that were 2 years younger than me. My wife, after 18 years of marriage converted to Catholicism and is now the best Catholic woman I know, ever knew next to the writings of Catholic Saints. Now I'm looking into the diaconate to continue what I still believe God is calling me to. All of that is a long story in itself.
Don't waste a lifetime trying to attract someone that simply is not attracted to you. Most relationships like you describe do not end up in marriage. By the way, the girl I was crazy about ended up divorced, living with another man out of state and does not consider herself a practicing Catholic - sounds new age now. She has no children and is completely self-absorbed as I realized early on still. Her father is laicized. Her mom is not practicing Catholicism anymore. and to top it off one of her sisters committed suicide and the family is still in denial, trying to accuse the spouse of murder. My family was equally messed up and God knew way before hand what would happen. And because I placed all of my trust in Him first, He delivered me from making the bad choices I made based on beauty, image and illusion. Let God lead you above all. Place Him first, give him a chance for a religious vocation and let Him bring someone to you instead. That's my 2 cents.:shrug:
BTW: We're working on 21 years of marriage, happy 95% of the time, more really, and have 3 beautiful children that love us both. They are God's wonderful blessing to us and are very sweet children, as told to us by everyone in the parish that sees them from a distance and up close. Give yourself to God first.