Actually, in Ordinatio Sacerdotalis, Pope John Paul II has already made clear the Church has not the power, even in theory, to ordain women as priests. This is not even a matter of Tradition, but of total lack of power of the sacrament to be conferred on women.
With regard to the Pope, I am pretty confident he would have known. It was no secret and since Pope Leo XIII was able to find out within weeks that Peru had passed civil marriage and licensture laws, which he swiftly condemned, I would be suprised if he had refrained from condemnation in this case, if he felt it was merited. The Paraguay constitution at the time only recognized sacramental marriages and any violation of this would have been duly noted by Rome. Today, the Paraguay constitution has since been amended to ban polygamy.
Again, as St. Thomas noted, the validity of the sacrament is not affected by having more than one spouse, since there is no impediment to the primary end of marriage, the rearing of children. However, the Church has generally opposed polygamy on the grounds that the tertiary end of marriage, the good of the spouses, is difficult if not impossible to establish with multiple wives and therefore an impediment to the good of the interior life of the spouses. Now, the primary purpose of the sacraments is the edification of souls through grace. The primary end of marriage (that which affects its validity) is not violated by polygamy. However, the tertiary end, which relates to the primary purpose of the interior life, would be threatened. This is much like an occasion of sin. It is not sin, but one should still strenously avoid it, that one not fall into sin.
Same applies here. The union of one man and one woman is the form most suited for the edification and growth of souls in marriage. Polygamy, while not invalid, does not assure this and therefore is not permitted. Just as a married man can be validly ordained a priest, the Tradition of the Church strongly indicates in the West, that, given the teachings of Christ and St. Paul on celibacy, the better vehical for the glorification and sanctification of souls is celibacy. This is true despit the fact that marriage is a good and not evil, it simply does not serve the primary ends of the priesthood as well as celibacy, and is therefore not permitted.
Hope this makes sense! And, you are correct, the Easterns do not permit the practice either, for the same reasons as the West.