I go with St. Augustine on the issue of ignorant or unknowing people(not negligent or discarding, but truly cut off and fully ignorant), like unbaptized babies or children cut off from the world in pagan tribes. They do not go to heaven, but they goto a pleasant peaceful place in Limbo free from pain and sadness. To say they goto heaven would be self-refuting because it makes ignorance out to be bliss and the Gospel to be a curse. St. Augustine wrote about this. I remember an apologist talking about the story of an Eskimo who got angry at a priest. The priest told him that people can goto heaven because of their ignorance of Christ, of which the Eskimo stated, "then why did you tell me!"..
I think you're seeing ignorance as a means of salvation. No one goes to heaven because of ignorance--they go to Heaven with the help of God's grace by repenting of their sins and submitting themselves unconditionally to Him by faith. We are saved by grace through faith, hope, and charity, not by perfect knowledge (as some Gnostics claimed).
Again, the person who doesn't want to know has a disregard for truth that will exclude him from salvation. Knowledge of the Gospel cannot damn someone who would otherwise be saved, it fulfills the desires of one who would otherwise be saved--it is a great blessing because it promises the fulfillment of of the hope they had and therefore strengthens them to remain on the true path, now brightly illuminated before them, and against the temptation to give themselves up to sin. Those who would be otherwise damned--since they are irrepentant of their sins and do not love God (but rather adore creatures, for which there is no excuse for that) or do not unconditionally desire to conform themselves to His way and truth (ie His Logos)--are confronted sensibly by the Word of God in word and action which may inspire and re-open their hearts to the movements of grace.
There is no situation where knowledge of the Gospel would cause one to go from the state of grace to the state of damnation because an ignorant person with the state of mind and will that would suffice for salvation would strive to conform themselves to the truth when known--one who would not conform himself unconditionally to the truth when known would not be disposed to salvation in the first place. However, those not disposed to salvation may, upon hearing the Gospel and experiencing the charity of others, be inspired to amend their ways by receiving the graces and promptings they had hardened their hearts to. Knowledge of the Gospel can never make an just man unjust, but it can make an unjust man just.
Furthermore, the problem with saying only some people are offered the grace necessary for salvation is that it is contrary to the universal salvific will of God.
As St. Alphonsus Liguori said,
"If then God wills all to be saved, it follows that He gives to all that grace and those aids which are necessary for the attainment of salvation, otherwise it could never be said that He has a true will to save all. " (The Great Means of Salvation, Part II, Chapter II)
St. Alphonsus further explains that Baptism of Desire is de fide (the decrees he cites, from Trent and Pope Innocent III--he is not named but the Canon Apostolicam is from him--came after St. Augustine):
But baptism of desire is perfect conversion to God by contrition or love of God above all things accompanied by an explicit or implicit desire for true Baptism of water, the place of which it takes as to the remission of guilt, but not as to the impression of the [baptismal] character or as to the removal of all debt of punishment. It is called “of wind” [“flaminis”] because it takes place by the impulse of the Holy Ghost who is called a wind [“flamen”]. Now it is de fide that men are also saved by Baptism of desire, by virtue of the Canon Apostolicam, “de presbytero non baptizato” and of the Council of Trent, session 6, Chapter 4 where it is said that no one can be saved “without the laver of regeneration or the desire for it.” Moral Theology, Bk. 6, nn. 95-7
Implicit desire is one where the person is ignorant of the thing to be desired, but would desire if it were known.
These truths above, that God offers all men the means of salvation and that perfect knowledge is not absolutely necessary for salvation have been made explicit and repeated by the ordinary Magisterium of Popes, a General Council, and various Roman Congregations often, especially in the last few centuries, not to mention being held morally unanimously--and probably actually unanimously--among the college of bishops (it is also commonly held by theologians, including Doctors of the Church and various other Saints). These pronouncements require at the very least the religious submission of mind and will, which itself requires a presumption of truth and a very, very good reason to suspend assent (not just preferring a counter-opinion). One can speculate as to what St. Augustine's response would be to such consistent direction from Rome and the entire college of bishops given his actions in other matters in his own time.