How does this address the "I am a man of my word, so I will keep my promise even though it leads to ends I don't like" criticism? Because that shows up an awful lot in stories with "Lawful Evil" characters?"
What do you mean by "stories with LE characters"? If you're talking about D&D novels, I'm not familiar with them (other than the first few Dragonlance ones, and that was a long time ago).
I think a person who sticks to his/her word no matter what is either LG or, if not concerned with others' wellbeing but only with keeeping his/her word, LN. An evil person can't be fully honourable - as per Gygax's PHB (cited upthread), a LE person scorns truth.
"The LE person cares for nothing but his/her own self-interest, thus the LE person cares for nothing but his/her own self-interest." You have yet to show that that is actually the meaning of Evil.
I cited Gygax's DMG (p 23) upthread: "Evil, on the other hand, does not concern itself with rights or happiness; purpose is the determinant."
Personally, I would think it is much more cogently defined as "places one's own interests categorically before the interests of others." Doesn't mean you can't be interested in others' welfare, just that they're never more important than you are.
That does not seem to me to be consistent with "not concerning oneself with rights or happiness".
Of course the standard sorts of cases can be set up which put on a degree of pressure: eg if A loves B, then A's self-interest can include helping B. Gygax's alignment scheme doesn't really handle moral systems that try to generalise this sort of self-regarding other-regard so as to generate general moral obligations.
What about those who see Law as an end in and of itself, something to be pursued because organization is inherently valuable...and who pursue it with ruthlessness and malice?
I'm not really sure what "malice" adds here - it seems like it's just emphasising the ruthlessness of the ruthlessness.
Ruthlessly pursuing law and order seems like LN to me. Per Gygax (running together p 23 of the DMG and p 33 of the PHB):
Those of lawful neutral alignment view regulation as all-important. It is the view of this alignment that law and order give purpose and meaning to everything. This is because the ultimate harmony of the world - and the whole of the universe - is considered by lawful neutral creatures to have its sole hope rest upon law and order. Without regimentation and strict definition, there would be no purpose in the cosmos.
Therefore, whether a law is good or evil is of no import as long as it brings order and meaning. Evil or good are immaterial beside the determined purpose of bringing all to predictability and regulation.
Upthread I've been saying that neither the LG or the LE regard law as valuable in and of itself. It's value is purely instrumental. The Lawful Neutral do regard law as valuable in itself - they insist on, and enforce, order whether or not it serves human wellbeing. This is why Gygax is able to say that the LN "tak[e] a middle road betwixt evil and good." They are not evil, because they recognise some external constraint upon the pursuit of self-interest (namely, law and order). But neither are they good, because they don't care about wellbeing, rights or happiness.
To use language that Gygax doesn't, one could say that the LN are rules-fetishists. They have mistaken a potentially valuable means (social order) for an end in itself.
In my view, this Gygaxian approach to alignment is coherent, though not useful for framing all moral conflicts. It captures a real conflict - namely, the social-theoretic disagreement over whether social order, or freedom and individualism, will lead to human wellbeing. And it provides labels for the nemeses of each view: the LE are the nemeses of the CG, because they realise the CG's worse fears about the consequences of social structures, while the CE are the nemeses of the LG, because they demonstrate the horrible consequences of untrammelled individual will. It also provides labels for those who mistake the means that are the focus of dispute for ends in themselves (the LN and the CN).
I recognise that this is not the aligment system found in Planescape, and probably not even that found in Gygax's PHB Appendix IV. But it has the benefit over them of being coherent and relatively straightforward in application, and in not purporting to capture all moral disputes but rather honing in one one particular site of conflict (social structure vs individualism).