Rationally, I cannot see a foot to stand on with this position. Any way of saying someone who's not a baptised Christian and doesn't even desire baptism could be saved seems like a direct contradiction of EENS. And yet even the largest Trad groups all teach the same. Even +Lefebvre taught that people in false religions can be saved. How is it that even those who claim to be rejecting V2 are still supporting this denial of EENS? Even groups that don't even claim communion with Rome at all, like the CMRI, still teach this. Only various independent individuals like the Dimonds seem to teach otherwise. Despite how obvious it is that EENS = EENS, it still seems like the overwhelming majority of clergymen, even those who claim to reject modernism and its associated heresies, still teach that those in false religions can be saved. "Implicit baptism of desire" or what have you. Why do they teach this?

I have heard some conjecture that those who die in the state of grace outside the Church (but united to Her), are relegated to limbo.  I’m not sure what the basis for this conjecture is, since limbo there was a limbus patrarum (limbo of the fathers in the OLD Testament times before Christ), and a limbus puerorum (limbo of children who die before baptism), but the proposition of yet a new third limbo would seem to be a novel invention.

You kindof contradict yourself here.  ACTUAL grace certainly does exist outside the Church.  Church actually has condemned the contrary.  But if you're saying that the moment a person enters sanctifying grace, then he is thereby within the Church, then there can only be sanctifying grace WITHIN the Church.  This is neither here nor there in terms of the main argument, but it's important.

I don't believe that God would allow someone in a state of sanctifying grace to leave this life without the Sacrament of Baptism.  I do believe, however, that there are many who enjoy a degree of natural happiness for eternity depending on the natural good or bad they did during their lives.  As the Church teaches, the sufferings of hell vary in proportion to how bad one has been in life.  If you have a naturally-virtuous person who lived his life doing good and avoiding evil, then that person most certainly does not suffer the same fate as a Judas Iscariot.  I believe that even adults can approach an eternal state that is very close to limbic happiness, at the very least entailing relatively light amounts of suffering, perhaps no more than one might experience during life on earth here.

I do believe that this is the major hangup some people have against not allowing NATURALLY-VIRTUOUS people to be saved, this vision of hell as a monolithic place where even a virtuous Jєωιѕн mother who gave her life for her children and was kind and generous to everyone in this life is playing checkers with Joe Stalin in a fiery cauldron for all eternity.  So people recoil at the "injustice" of such a thought.  But the Church itself in one of the EENS definitions clearly states that the degree of suffering varies in proportion to how souls conducted themselves in this life.

1.  As Lad said, actual graces exist outside the Church.
2.  One is only "joined" to the Church he if is a member.  Non-members are not "joined"; this is a modernist ideal.
3.  One cannot be in the state of sanctifying grace, unless he is 1) repentant of his mortal sins (if any), 2) receives remission of Original Sin.
4.  Contrition for one's sins, no matter how perfect, cannot remove Original Sin from one's soul.  Ergo, the unbaptized cannot attain sanctifying grace apart from Baptism.
5.  Baptism here defined means the actual sacrament, or the desire of it (accompanied by the desire to enter the Church and an acceptance of the Trinity/Incarnation, at minimum).
6.  All actual graces that an unbaptized person receives through an act of contrition are given that they may seek out and accept the Church, only through which they can be saved.
7.  An unbaptized person who dies repentant for their sins, but not desiring of the Church or baptism, would go to Limbo as they cannot enter heaven with Original Sin on their souls.

7.  An unbaptized person who dies repentant for their sins, but not desiring of the Church or baptism, would go to Limbo as they cannot enter heaven with Original Sin on their souls.

Only children who die unbaptized before the age of reason go to Limbo.

There are however different degrees of punishment in hell.

My understanding is that Limbo is a part of hell, so you're describing the same place.  Hell's main punishment, strictly speaking, is the absence of God, so those who are in Limbo do suffer this loss, even if they suffer no physical torment.