That's an entirely separate question ... whether or not he can be saved.  He cannot, however, merit salvation by any acts of natural virtue, but I hold (and you seem to agree) that he can offset some of his eternal suffering by the exercise of natural virtue.

I just would not say they are in Limbo, since Limbo is reserved for a place of non-punishment but merely deprivation of the beatific vision.

1) one man steals $1,000 and dies unrepentant
2) another man steals $1,000, repents, returns the $1,000, and then gives another $10,000 to the poor to make up for this.  Then he gives up his life to save another person.

Are you trying to claim that the punishment of both of these is the same?

Well, I would disagree with that. What you are saying is that non-meritorious, non-supernatural (purely natural) acts can be satisfactory. But that is a mistake. What you can say is that, a naturally good person, would have perhaps many attenuating circuмstances in the one or two mortal sins that he committed, so that his eternal punishment would be less than one who sinned out of pure malice, and repeatedly. Still sobering. But all the acts of natural virtue in the world combined cannot equal one meritorous action. And in order for a good work to be satisfactory, Ladislaus, in addition to being meritorious, Theologians commonly teach, it must in some way be painful. Our Lord made Infinite Satisfaction for all our sins by His Infinite Merits and His Incredible Sufferings. Our Immaculate Mother Mary, Whose merits are next to His, made the next greatest satisfaction. All in the State of Grace, and only those in the State of Grace, I would hold, are capable of making satisfaction.

But if this person avoids sin and corresponds to Grace, and is ready to seek the Truth, God will enlighten him about Christ, and save his soul. St. Alphonsus says that.

If these were only natural acts, they would not suffice for salvation, nor either for expiation, reparation and satisfaction. At most the second could have been less culpable to begin with, owing to his naturally good life, and thus have less punishment, for natural virtue cannot expiate either guilt or punishment of mortal sin by itself. But then again your scenario is a hypothesis. Hear St. Alphonsus, on what a non-Christian should do, in order to receive the saving knowledge of the Truth, Who is Christ: the Scriptural example of Cornelius is given. Recall Cornelius gave alms and helped the Temple, avoided sin and prayed. Hence, God enlightened him, both by an Apostle and by an Angel, and saved his soul: "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 [St. Thomas], 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.” https://exlaodicea.wordpress.com/2017/01/23/st-alphonsus-liguori-on-st-thomas-on-the-necessity-of-explicit-faith-in-the-trinity-and-the-redeemer/

But if this person avoids sin and corresponds to Grace, and is ready to seek the Truth, God will enlighten him about Christ, and save his soul. St. Alphonsus says that.

What you are saying is that non-meritorious, non-supernatural (purely natural) acts can be satisfactory. But that is a mistake.

If they are in good faith, and fulfil the required conditions, they can and will be saved, though not as they are. They will come to Christ at some point in their lives, and thus be saved as Christians Catholics.