I've never really tried to clean up the concept, because I dont really have an issue with the alignment system (and I love the great wheel that depends on it really) anyway.
Personally, I prefer Righteous vs Pragmatic and Disciplined vs Spontaneous. Note that this implies that any of the nine resulting alignments can be "good" or "evil"--a Righteous Disciplined person may simply
view themselves righteously, or act as though certain principles of morality are paramont, while still doing ridiculously evil things. (I would even say that
many of the most evil people who have ever lived saw themselves as righteous!)
Righteousness vs Pragmatism is the "what" of moral action: what is worth doing, what costs are acceptable, what results are desirable. Most "Evil" characters in D&D are actually Pragmatic ones, who prioritize efficiency and success over doing things the "right" way. The best representation of the difference is the "who you are in the dark" scenario: a pragmatic individual will give a frank evaluation and say, "if there are no consequences, then I should do whatever is most advantageous," while a righteous individual would say, "even if I could know for sure no one else would know,
I would know it was Just Wrong." Fundamentally, Righteousness says some acts are virtuous (or villainous) in and of themselves, and should thus be pursued (or avoided), while Pragmatism says that (in principle) nothing is verboten, it's the costs, impacts, and consequences that set those terms.
Discipline vs Spontaneity is the "how" of moral action: how should we carry out our goals (whether they are righteous or pragmatic or neutral). This one maps more cleanly to Law vs Chaos, but is not a perfect fit, since you can have a Chaotic person (Chaotic because they oppose
socially-enforced rules) who upholds a code of personal honor (Disciplined), and you can have a Lawful person (Lawful because they help enforce and support the legal apparatus) who takes a "living law" attitude that laws can and should be interpreted differently if meaningfully different situations arise (Spontaneous). Demonstrations of this can be found with stuff like the "Soldier vs Warrior" or "Technician vs Performer" tropes: one is precise and regimented, the other is passionate and dynamic. Fundamentally, Discipline says an organized, structured, "proper" approach is required for meaningful success lest you waste your efforts, while Spontaneity says that every rule will have exceptions and every pattern will have holes, so it's best to refine your ability to adapt and choose whatever makes sense in each situation.
The Paladin, obviously, is still in general Disciplined Righteous, but it is entirely possible to have a Spontaneous Pragmatic Paladin, you just have to work harder for it. (Some might argue Yoda is akin to this kind of character.) A Righteous Spontaneous person may hold that some actions are inherently morally dubious, but the best way to combat such things is to keep your options open--sure, murder is bad, but forcing
everything to go through the proper channels and due process can let the guilty go unpunished and the innocent suffer.