Are there truly invincibly ignorant persons?

Perhaps not.  Consider this from the First Vatican Council:
To this witness is added the effective help of power from on high. For, the kind Lord stirs up those who go astray and helps them by his grace so that they may come to the knowledge of the truth; and also confirms by his grace those whom he has translated into his admirable light, so that they may persevere in this light, not abandoning them unless he is first abandoned.
So, the First Vatican Council is saying that the omnipotent One and Triune God wants anyone "who goes astray" (e.g., non-baptized Catholics -- Protestants, Orthodox, Coptics, etc.) to "come to the knowledge of the truth" (i.e., Catholicism). In light of this, we must ask ourselves if there are, in fact, any truly "invincibly ignorant" persons, and if not, then Vatican II must have been describing an "empty set" (e.g, "The set of squares with 5 sides", "The set of integers which are both even and odd", etc.) when it spoke of "those who, through no fault of their own..."  While, perhaps, theologically correct, Vatican II's teaching simply does not describe the Creation which the One and Triune God has established and His omnipotence over and within it.

Consider, also, these Magisterial statements:
"We declare that a great number of those who are condemned to eternal punishment suffer that everlasting calamity because of ignorance of those mysteries of Faith which must be known and believed in order to be numbered among the elect." (Saint Pope Pius X, Acerbo Nimis)
"We answer the Semipelagians, and say, that infidels who arrive at the use of reason, and are not converted to the Faith, cannot be excused ... St. Thomas explains it, when he says, that if anyone was brought up in the wilds, or even among brute beasts, and if he followed the law of natural reason, to desire what is good, and to avoid what is wicked, we should certainly believe either that God, by an internal inspiration, would reveal to him what he should believe, or would send someone to preach the Faith to him, as he sent Peter to Cornelius. 

Thus, then, according to the Angelic Doctor, God, at least remotely, gives to infidels, who have the use of reason, sufficient grace to obtain salvation, and this grace consists in a certain instruction of the mind, and in a movement of the will, to observe the natural law; and if the infidel cooperates with this movement, observing the precepts of the law of nature, and abstaining from grievous sins, he will certainly receive, through the merits of Jesus Christ, the grace proximately sufficient to embrace the Faith, and save his soul." (Saint Alphonsus)
Q. What are we to think of the salvation of those who are out of the pale of the Church without any fault of theirs, and who never had any opportunity of knowing better?

A. Their inculpable ignorance will not save them; but if they fear God and live up to their conscience, God, in His infinite mercy, will furnish them with the necessary means of salvation, even so as to send, if needed, an angel to instruct them in the Catholic Faith, rather than let them perish through inculpable ignorance. (Familiar Explanation of Christian Doctrine by Rev. Michael Müller, CSSR)