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Initially the thinking was that Heaven vs. Hell were a strict BINARY condition.

But even the Church gradually adopted the notion of a Limbo (for infants at least).

So then eternity would consist of 3 states:

Heaven
Limbo
Hell

And even in hell there are many degrees.

But how about we look at it this way.

SUPERNATURAL
NATURAL

SUPERNATURAL is the Kingdom of Heaven in the interior Life of the Holy Trinity

Meanwhile the NATURAL state is, rather a continuum, going from those who are naturally happy (like unbaptized martyrs, to unbaptized infants, to those, perhaps less happy, such as those who were justified but not saved, to those who suffer in varying degrees depending on the balance between their virtues and their sins, right down to the devils who suffer the most).

So perhaps those American Indians who lived naturally virtuous lives do get to go to a "Happy Hunting Ground" of sorts, as they believed.  Perhaps all happiness and suffering in Hell is in fact relative.  Even the dogmatic EENS definitions refer to the varying degrees of suffering in Hell.

This would then relieve the pressure against EENS from all those sentiments which wrongly imagine a naturally virtuous Jєωιѕн grandmother who perhaps sacrificed her life for her children suffering the same fate as Joe Stalin or Judas.

I believe that it is this misconception of Hell that has people recoiling against EENS and grasping for straws looking for a BoD.

While the Beatific Vision cannot be earned and is beyond the created capacity of human nature to experience, it is given as a free gift by God irrespective of merit.  It cannot be earned, but is a pure honor, a pure glory.

Right.  That's exactly why Catholics have to pray for "final perseverance" because we don't know what will happen, if we will prevail, at the hour of our death.
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But, apparently, for BOD'ers, the hour of death is a walk in the park.  And any old non-catholic can "wish upon a star" for heaven, and be granted it, whether a priest is present or not.  Whether they've been baptized or not.
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Christ gave us an entire sacrament wholly dedicated to the last hours, yet a non-catholic can waltz into heaven, just based on a desire for God.
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Salvific-BOD theology has more holes than swiss cheese.  Sure, BOD can justify.  But can it save the unbaptized?  No, it just doesn't stand the test of catholic sanity. 

St. Augustine:

When any die for the confession of Christ without having received the washing of regeneration, it avails as much for the remission of their sins as if they had been washed in the sacred font of baptism.

St. Augustine also says that martyrdom results in a washing or "remission of their sins" (he defines "washing" here).  He was instructed by St. Ambrose who clearly distinguished between the washing and the CROWNING.

There in fact TWO effects of Baptism:  1) the washing of sins and 2) membership in the Church through the "crowning".

Another word used by the Fathers for this other effect is "the seal".

I hold that martyrdom (perfectly) and desire (imperfectly depending on the degree of the desire) can supply the one effect of Baptism, but not the other.  Most theologians agree that BoD and BoB do not confer the character of Baptism.

Ladislausian soteriology holds that, even while BoD and BoB suffice for the remission of sins, they do not suffice to enable souls to receive the Beatific Vision (the crown and the glory).  Consequently, they can justify to varying degrees, but they can never save (i.e. allow entry into the Kingdom of Heaven).

Unbaptized martyrs, therefore, end up in a place of Limbo, and those with the intention to receive Baptism can receive various degrees of remission proportionate to their votum for Baptism.

At some point after the Fathers, theologians generally lost their grip on the meaning of this "character" of Baptism, reducing it to a mere non-repeatability marker that some people in heaven have and others don't.  Ladislausianism rejects that understanding.

As with the Priesthood, this character renders the soul into the likeness of Christ, so that the Father recognizes them as His own (adopted) sons into the life of the Holy Trinity, almost as adopted members of the Holy Trinity.  It is also the supernatural faculty which allows the soul the capability to see God as He is, in the Beatific Vision, a faculty with human beings lack in their created nature.