By contraception the Church means taking an action to sterilize the marital act. CI sterilizes the marital act. NFP does not. NFP is not contraception at all, as the Church understands it. Regulation of birth for serious/just reasons is licit; the methods of achieving that are total abstinence or partial abstinence (NFP). The effectiveness of the method is not relevant; it is the method itself that disorders the act (i.e., sterilizes what was supposed to be fertile - - as in CI and other forms of contraception).
I do not think the Church understands sex to be either a) only for procreation or b) for recreation at all. I think the Church teaches that the purpose of marriage, and the marital act, are procreation and to unify the spouses. Strictly speaking the pleasure is not the purpose. The procreative and unitive parts always go together, and it is disordered to separate the two, since that is the way God designed us.
Genesis 38:8-10 appeared in your comments earlier in the thread, and you state what you think it means. Have you investigated what the Church traditionally understood it to mean? Perhaps consider who has the authority to authentically interpret Scripture, you or the Church.
By the way, kudos to you for being humble and obedient to a teaching that you trying to understand.