I have no expectation that the following will answer the OP’s issues. And I will admit, up front, that I’m a rather shallow person and not well versed in complex theological matters.
But
Either Jesus gave the Church the authority to instruct with authority or He didn’t. If He didn’t, then the Catholic Church is just another Christian sect, having no more meaning or importance that the Westboro Baptist Church. But if He did, then we have a moral obligation to assent even to those teachings to which we do not agree. Not to do so is sinful.
Possibly my view of sin is inexcusably shallow, but I don’t think of it as something irremediable. I do, however, think of it as something that absolutely must be faced honestly. If the Church says artificial contraception is sinful, then it is. If I do it anyway, then I’m sinning, and must deal with the fact of my sinning.
I think it was historian Kenneth Clark who, comparing the Middle Ages and Renaissance with today, remarked that compared to those people in those eras, moderns “…neither sin well nor repent well…” We don’t sin well because we don’t face the fact that we are simply doing wrong through the act of our own wills. We make excuses, we cavil, we dissent.
No, we should “sin well”. We should admit what we’re doing and, if our will is set on it, do it in full knowledge of its wrongfulness. Then, to “repent well”, we need to admit to it, confess it, at least attempt amendment.
We expect ourselves to be blameless, or at least want to think of ourselves that way. But we’re not, and we never will be. I think maybe it was Chesterton who remarked that the Catholic Church “…is for saints and sinners. For the merely respectable, the Anglican Church will do…”
I, for one, know I’m not a saint, so I am surely a sinner. Didn’t Jesus say even the just man “…falls seven times a day…”? And so, if I fall seven times a day, as Jesus says I do, perhaps I should be looking for those seven events (or more) and spend time examining my life to see those ways in which I sin, instead of trying to figure out a way to think I’m not sinning at all.
And so, if I do not find a way for my mind to rationally conclude that, yes, contraception is wrong (there are plenty of indications that it is) then what’s my duty as a Catholic about that? Well, it’s to assent anyway, to admit I’m in the wrong if I do it, to confess it and to at least make some effort at not doing it. Perhaps if I “sin well” in that regard, then I can also “repent well.”
Is it a challenge to assent to Church teachings even when my own reason refuses to accept them? Of course. But I do have a choice. I can either accept those teachings and be Catholic, or not accept them and be something else.