In the approach I find in those descriptions, LG is not a compromise between lawfulness and goodness - it is a claim/conviction that good can best, perhaps only, be realised by means of social order. Conversely, CG is a claim/conviction that good can best, perhaps only, be realised via relatively unconstrained self-realisation. Neither of these claims would make sense if we already knew that both law and chaos are self-standing values in their own right that dilute goodness.
They'd make sense as arguments directed at a neutral good character, or at eachother, for that matter. Good is the common ground. If a CG were trying to convince a CN of the rightness of CG, he might argue that only when everyone embraces the respect for others implied by Good, can each individual be secure in his own freedom. There's gradiations of alignment in AD&D, too. Not just LG, but L(N)G or LG(N) or (L)NG, etc... All those goofy outter planes. So you can be LG but put either Law or Good first. If Law, then Good is the best way to create a stable, Lawful society (folks are less likely to rebel), of Good, the Law is the best way to achieve a Good society.
Maybe it was a stretch, but I always saw the ethic axis as being as important as the moral. Maybe because OD&D just had Law/Chaos.
LN just cares about order, honor, and sticking to some arbitrary idea of what is proper, particularly his own personal honor, his own proper behavior, and being part of an order of some sort (a society, religion, heirarchy, whatever). He'd see an LE society as corrupt, and LG one as soft.
CN just cares about personal freedom, particularly his own personal freedom. He doesn't want anyones freedom abridged, and certainly wouldn't do so himself, but he doesn't feel obligated to prevent it, just avoid it on his own behalf. He'd see a CG as foolishly abridging his own freedom to help others, and a CE as foolishly abridging his own freedom out of spite & cruelty.
I also think mere amorality undersells the supernatural evil implied by early D&D. Evil is a detectable force, and being evil means you'll take damage from things that wouldn't harm a good person. That's pretty objective, and implies opposition, not just failure to rise to a moral standard. Not merely amoral, but actively immoral.
Taken that way, Evil doesn't just disregard the 'weal' of others, it resents it. Supernatural Evil doesn't ever commit 2nd degree murder, because they care too much about the suffering of others to have even depraved indifference, it's always with plenty of malice.
TN might be amoral and unethical - perhaps merely self-interested or weak or perhaps philosophically obtuse with moral/ethical relativism or obsessed with balancing the titanic ethic and moral forces threatening to tear the world apart.
Another point I remember being made about alignment in 1e is that the same alignment doesn't mean the same goals. Two LG kingdoms might still go to war, for instance. Maybe over a point of honor, a difference in religion, a desperate lack of resources - maybe because one views conquest as the only sure way to impose their vision of good on the other.