Since no one has given this information yet, I will submit an answer to my own question.
There are many different views that Christians have regarding the fate of those who have never heard the gospel. See these two Wikipedia articles:
Many of the original ideas were developed in the Catholic and Eastern Orthodox traditions. The idea is that all people are born under Original Sin and therefore do not a priori get to go to Heaven. Authors like Dante portray Virtuous Pagans who lived before Jesus as not even able to get into Purgatory but are in the first circle of Hell.
The Roman Cathecism issued by the Council of Trent, based on the opinion of Thomas Aquinas, believe that they may have been in Limbo (http://en.m.wikipedia.org/wiki/Limbo) and the virtuous pagans would have been caught up to Heaven during the http://en.m.wikipedia.org/wiki/Harrowing_of_Hell by Jesus in the three days between the crucifixion and resurrection.
Clement of Alexandria taught a similar doctrine, saying "It is not right that these should be condemned without trial, and that those alone who lived after the coming should have the advantage of the divine righteousness."
Jesus himself says things like the passage in John 15:
"If I had not come and spoken to them, they would not be guilty of sin; but now they have no excuse for their sin. Whoever hates me hates my Father as well. If I had not done among them the works no one else did, they would not be guilty of sin. As it is, they have seen, and yet they have hated both me and my Father."
This implies that those who do not hear the gospel may not be guilty of sin. John speaks of Jesus as a Paraclete (intercessor and comforter) in John 2:1 and then of the Holy Spirit as a Paraclete (comforter and teacher) in John 14:16, implying that Jesus is the first and primary Paraclete.
In short, it is indeed possible that Premise 2 in the list is wrong: one does not have to hear about Jesus to be saved. However, this still doesn't take care of the contradictions in every case, if not everyone winds up in Heaven. For that, we must investigate further.
Calvinism (and classical Armenianism) holds strongly to Paul's doctrine of Original Sin and furthermore says that salvation is ultimately decided by God in advance, and does not depend on human decisions at all. They would point to epistles of Paul such as Ephesians 2:8
"For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God— not by works, so that no one can boast. For we are God’s handiwork, created in Christ Jesus to do good works, which God prepared in advance for us to do."
Molinists (such as William Lane Craig) on the other hand believe that God knows what a person would choose in any given situation. They point to passages like Matthew 11:20-24
"Then Jesus began to denounce the towns in which most of his miracles had been performed, because they did not repent. “Woe to you, Chorazin! Woe to you, Bethsaida! For if the miracles that were performed in you had been performed in Tyre and Sidon, they would have repented long ago in sackcloth and ashes. But I tell you, it will be more bearable for Tyre and Sidon on the day of judgment than for you. And you, Capernaum, will you be lifted to the heavens? No, you will go down to Hades. For if the miracles that were performed in you had been performed in Sodom, it would have remained to this day. But I tell you that it will be more bearable for Sodom on the day of judgment than for you."
Here again we see Jesus supporting the idea that the amount of revelation plays a vital role and determines the consequences.
We have seen Jesus teach twice now that people who were exposed to miracles and his direct teachings and nevertheless reject them are held more responsible than those who didn't.
We see that Abraham's faith was counted to him as righteneousness, and of course we know that Abraham was God's friend and had experienced God's revelation directly. Because of this direct experience and revelation, he was willing to stop relying on his reason and go up to sacrifice his son Isaac. From this we learn once again that the level of personal experience and revelation plays a crucial role in judging someone's actions.
In my opinion, it is very hard to resolve the contradiction between "God desires all to be saved" and the reality that not everyone is saved. It seems to me that human decisions somehow play a role. But for the Molinist, Calvinist etc we still have the question of WHY God would place people in situations where He knows they will choose to sin. And for everyone else there is the question of God hardening Pharaoh's heart, or using sinful actions (such as Joseph's brothers throwing him in a pit, or David's sleeping with Bathsheba and getting her husband Uriah the Hittite killed in battle) to bring about great things later in in the story. What happens to these imperfect people after they die?
Consider 1 Peter 4:
"But they will have to give account to him who is ready to judge the living and the dead. For this is the reason the gospel was preached even to those who are now dead, so that they might be judged according to human standards in regard to the body, but live according to God in regard to the spirit."
My own personal opinion is that there is Purgatory and everyone is cleansed for a finite amount of time before they can enter the Kingdom of God. Jews have to follow the Law of Moses as described in the first five books of the Bible, as this is the Eternal Covenant of God with the Jews. Gentiles have only to observe the http://en.m.wikipedia.org/wiki/Seven_Laws_of_Noah
I think there is strong support for the above requirements for Jews and Gentiles found in Acts 15. It includes an official communication from the Church to all "Gentile Believers" (their words) from James the Just. See interpretations here: http://en.m.wikipedia.org/wiki/Council_of_Jerusalem
But as for the soteriology, there are many opinons and no one really knows. My own personal opinion is that many people can get saved without having heard the gospel. They are judged and can atone for their sins in what is translated as "hell" but is "geol" or "gehinnom" in the original.
I guess in some respects I am a Christian Universalist:
Other Universalists include groups like http://en.m.wikipedia.org/wiki/Seventh-day_Adventist_Church
At the end of the day, my answer to the question is that either God doesn't really desire all to be saved -- because He ultimately is capable of creating a world where everyone is saved -- or He desires all to be saved, in which case everyone is eventually saved.
My personal view is that being saved means eternal reconciliation to God and being in the Kingdom of God forever. Since God is all good, and just, and merciful, it seems very strong to me that God will save everyone who desires to be saved, or would have desired it if they had the choice. Even if they had incomplete information, they will eventually be saved. They may have to pay for their sins but eventually everyone will be in the Kingdom of God forever who would have wanted to be in it if they knew what that meant.