Here are some extracts from your quotes:
Elysium is the plane of ultimate good, unsullied by the concerns of hierarchy or anarchy . . .the driving force of Elysium is goodness and goodness only. Order or anarchy - it doesn’t matter, as long as it’s for the good. . . .The layers of Hades are called the glooms of Hades. This is an adequate description of the nature of evil at its worst. . . .
From the point of view of a paladin, these descriptions of Elysium
can't be true. Because from the point of view of a paladin, a concern for lawfulness/order does not
sully good, but is a necessary condition of achieving it. The paladin doesn't regard him-/herself as less than fully good!
Actually, unless the paladin is delusional they likely realize they're less than fully good by their very nature as a mortal, regardless of their specific alignment. On a temporal scale, I'm not sure any mortal creatures can really be "fully" good, evil, lawful, or chaotic. Even a paladin can be tempted to sin or fall from grace (indeed, it's a major archetype). So no paladin is fully good.
Celestials are another matter. They're
essentially good by their very nature and while they
can fall, it's a
much rarer occurrence than the fall of a paladin, just as it's much easier for a criminal to turn a new leaf and reform than it is for a fiend to become good.
Again, you're confusing how alignment works on a temporal/individual scale vs. a cosmological/wider one. Pure neutral good is more good than pure lawful good and pure lawful neutral is more lawful than pure lawful good; that's how the cosmology works. An archon is less fully good than a guardinal and less fully lawful than a modron. But a paladin is
not necessarily less fully good than a neutral good cleric or less fully lawful than a lawful neutral druid, because neither the paladin, the cleric, nor the druid are essentially good or lawful: their behavior doesn't have to be 100% consistent with an idealized version of their alignment (whereas an archon, guardinal, and modron do by default).
Three lawful good characters may exhibit differing degrees of lawful and good behavior, despite possessing the same basic alignment. One might be more willing to overlook the laws of society when an innocent's life is at stake where another believes the law must be obeyed at all time except in the direst circumstances. Another might see things through a more nuanced lens, leaning toward neither law nor good particularly. A good example are Roy Greenhilt, Durkon Thundershield, and Miko Miyazaki in
The Order of the Stick: Roy's obviously more good-leaning than lawful (but is still overall lawful good) while Miko's priorities clearly favor law over good (but again, she's still good enough to be LG); Durkon falls somewhere in-between.
The conflict between the priorities of law and good actually
is a canonical feature of lawful good characters, as others have pointed out (just as chaotic good characters must balance their desire for freedom from authority with their desire to do good). Each alignment has its strengths and its faults, even neutral good (arguably naivete or indecisiveness).
The description of Hades makes no sense either: why is the gloom of Hades worse than the Abyss, where demons rend each other, plus visitors, limb from limb? How does the chaotic violence of the Abyss mitigate the evil there?
Again, this comes back to my earlier discussion of which you find worse: inescapable but perfectly stable tyranny or a perilous world of endless strife but absolute free will. A lawful good and a chaotic good character's answers might differ substantially on this question, but canonically D&D says the answer is neither: the worst possible world is one where there is no hope at all, which is exemplified best by the Gray Waste of Hades.
A relevant point can be found in the
Book of Exalted Deeds:
BoED said:
If the most soullessly evil villains relish spreading despair and devouring every last shred of hope, it naturally follows that the cause of good involves rekindling hope in the face of despair. This might be the most nebulous of all good deeds, hard to define or measure, but it might also be the heart and essence of good. All the other good deeds discussed in this section, in addition to their often concrete and physical benefits to people in in need, have the additional intangible benefit of increasing hope. A man whose body is wasting away from disease actually has two illnesses: the physical disease that consumes his flesh and the despair that gnaws at his soul. Healing him not only heals his body, it also restores his lost hope. A woman who throws herself on a paladin's mercy and turns from her evil ways struggles along the difficult road to redemption. The paladin's mercy and forgiveness offer the most important assistance along that road, a vision of the reward that lies ahead.
Hope in its truest form is more than just a vague wish for things to be better than they are; it is a taste of things as they might be. When an exalted bard comes to a city that groans under the oppressive rule of a pit fiend, he may inspire hope by singing tales of liberation or by demonstrating force of arms against the pit fiend's diabolic minions. But the best hope available to the oppressed residents of the city is when the bard simply shows them kindness, thereby reminding them of what it was like to live under a more benign rule. He brings them together in a community, whereas the devil have been turning them against each other, sowing distrust along despair. By experiencing a taste of kindness and freedom, however small, the citizens are inspired with hope. The hope empowers them to resist the devils, with or without the bard's force of arms.
This is an extremely idealistic (in the sense that it's literally idea-based rather than concrete) sense of good and evil, but it's the one D&D runs with. A villain who deprives the heroes of hope and leaves them wallowing in despair is worse than one who simply kills them. A hero who has hope might triumph over extremely long odds; a hero who is convinced there is no hope might fail even when the task they face isn't particularly insurmountable. A person kept alive but in a state of constant misery and despair suffers more in this view than one who dies quickly but with a shred of hope that evil will fail. From that perspective, the glooms of Hades, which literally sap a good character's capacity of hope from them, is worse than the Abyss or the Hells.
From Gygax's DMG, p 41:
Basically the degree of evil (faint, moderate, strong, overwhelming) and its general nature (expectant, malignant, gloating, etc) an be noted.
Again, however, the spell distinguishes the degree of evil not by the actual moral weight of the individual in question but rather by how supernatural that evil is.
Here's what the 3rd edition
Player's Handbook says:
PHB (3) said:
Aura Strength: An aura's evil power and strength depend on the type of evil creature or object that you're detecting and its HD, caster level, or (in the case of a cleric) class level.
The following table (which is difficult to replicate here) explicitly has a hierarchy of regular evil creatures < undead < evil outsiders / clerics of evil deities. Basically, an extraordinarily cruel orc warrior scores a lower level of evil than even a neutral cleric of an evil deity, because that cleric channels the power of an extremely powerful and supernatural source of evil. The
detect evil spell does not actually distinguish the individual evil of a character - only how supernatural it is.
The 5th edition
Player's Handbook goes even less far: it just tells you if an aberration, celestial, fey, fiend, or undead is within a certain range and doesn't even distinguish between them the way the 3rd edition version of the spell does. So again,
detect evil (and good) is very general in its use, rather than a highly sophisticated evil-o-meter.