As we saw in that earlier post, the Church has already settled this debate. Couples may morally have recourse to the God given infertile periods of a woman's cycle. Roma locuta est, causa finita est. The infallible teaching of the Church was affirmed by Paul VI in Humanae Vitae
If therefore there are well-grounded reasons for spacing births, arising from the physical or psychological condition of husband or wife, or from external circumstances, the Church teaches that married people may then take advantage of the natural cycles immanent in the reproductive system and engage in marital intercourse only during those times that are infertile, thus controlling birth in a way which does not in the least offend the moral principles which We have just explained." (16).
And just in case you might be thinking "that's post Vatican 2" here is Pius XII in 1951 from an address given to midwives:
If the application of that theory implies that husband and wife may use their matrimonial right even during the days of natural sterility no objection can be made. In this case they do not hinder or jeopardize in any way the consummation of the natural act and its ulterior natural consequences... the moral lawfulness of such conduct of husband and wife should be affirmed or denied according as their intention to observe constantly those periods is or is not based on sufficiently morally sure motives...Serious motives, such as those which not rarely arise from medical, eugenic, economic and social so-called "indications," may exempt husband and wife from the obligatory, positive debt for a long period or even for the entire period of matrimonial life. From this it follows that the observance of the natural sterile periods may be lawful, from the moral viewpoint: and it is lawful in the conditions mentioned.
Something that you seem to be overlooking is that, far from being immoral, the NFP is morally neutral. NFP is simply a way of gaining and keeping track of knowledge about a woman's cycle and can be as easily used to get pregnant as it can be used to avoid pregnancy. The Church allows the use of God ordained infertile periods for reasons stretching from child spacing and financial woes to life jeopardizing medical conditions.
Further, NFP can never be used as contraception. Contraception is, by the very etymology of the word, an action against conception. Contraception, because it perverts the sexual act (not because it reduces the number of children a couple may have) is always immoral. NFP, which doesn't pervert the sexual act, is never intrinsically evil. A given couple can, when "serious reasons" are not present, use NFP selfishly and even immorally, but NFP in and of itself isn't, indeed can't be, immoral.
The same distinction is made between drinking wine and smoking crack cocaine. One can misuse wine to get intoxicated and to do so is immoral. But drinking wine in and of itself isn't immoral (as we see from Jesus' own example) because wine can be used in moderation. Smoking crack cocaine, on the other hand, is immoral and is never morally permissible because it always results in a loss of reason ("getting high").
NFP, like wine, can be used for moral purposes or for immoral purposes. Contraception, like crack cocaine, is always immoral because it always results in a perversion of the sexual act.