All fine and dandy until you start prying under the hood of your deontic and consequentialist systems.
Can wrong actions ever be justified? And, if not, how do you deal with conflicting duties? (Well, maybe that could be the primary distinction between Lawful Neutral and Lawful Good--lawful neutrals are more willing to muddy their hands with actions they believe to be wrong but necessary while lawful good characters are inclined to say that wrong actions are never necessary--as such things go, it's a distinction that fits the alignments pretty well). On the other hand, exactly what our duties are would be a the five million dollar question because it would certainly be possible to have a very loose doentology that neither prohibited nor mandated very much at all. (Some ancient systems may have been like that in their popular forms--don't betray hospitality, don't kill your kin, don't blaspheme, and that's pretty much it. It would certainly fit with the groups traditionally labeled chaotic).
For consequentialism, are we talking a rules-consequentialist approach or an individual consequentialist approach? So, if there is an action which, if taken by one person only or a small group of people increases the total good but which, if followed by everyone would destroy more good than it creates, is it right or wrong by the consequentialist system? (The example in my philosophy book was breaking water rationing by keeping a rose-garden during a drought--if one person does it, the excess water used doesn't amount to enough to significantly harm the whole community and we can stipulate that the beauty and pleasure of the rose garden are goods that exceed the insignificant detriment; on the other hand, if even a significant minority decide to ignore the water rationing, there will be great harm as there isn't enough water to go around).
At the point you pull off the hood and start examining the various deontic and consequentialist systems in detail, you find that, depending upon the consequentialist system you choose, you may end up with chaotics that are nearly indistinguishable from lawfuls in terms of action. In fact, you may find that they are even less flexible than your lawfuls. (One criticism of utilitarianism--particularly in its radical forms is that it leaves no freedom for personal interests ("a philosophy for angels rather than men" was how Fr. Richard Neuhaus put it). Playing D&D, for instance would be verboten in some radical utilitiarian systems because more good would be created if all the players were helping in soup kitchens somewhere.)
So, I'm not certain that the switch would actually get you the consistency you're looking for.
I also don't exactly see how you would fit evil alignments into the schema. Lawful evil (or people we would label as Lawful Evil since real life doesn't come with alignments) people don't generally do evil because they believe it's their duty. Nor do people we would label as chaotic evil do evil because it brings the most pain to the greatest number (in fact, their actions generally could do more harm if they exercised a bit more discipline). Rather, evil people, are generally trying to accomplish their goals--money, sex, power, honor, etc without regard to the morality of their actions. But that doesn't lend itself toward division across the deontological/consequentialist divide.
So, as for good and Lawful Neutral outsiders, I would say this: deontology and consequentialism are both sufficiently flexible that you could play them pretty much without any changes except for how you word their arguments and admonitions. In fact, you could even make the Lawful ones consequentialist too without requiring you to change anything. For slaadi, however, you'd be hard pressed to call them sloppy consequentialists or to fit them into your scheme at all. They are far more akin to a force of entropy than consequentialism. And demons, devils, and yugoloths won't really fit into either scheme (though I suppose, when treating them as tempters, you could use deontological rationalizations for devils and consequentialist rationalizations for demons).
