Benefit or harm to random others is an irrelevant side effect.

This in itself is evil, because it puts the interests of others below your own. The old school characters were 'neutral' because they either still cared about someone in the end (even if it was their friends only), because they still drew a line somewhere when exploiting others, but mostly because they existed in the same books as comically evil kill-everyone villains and demons and it was easy say "well they are not as evil as Yeenoghu, so neutral it is"

social climbing boot licker

This one would not necessarily be chaotic, after all a social hierarchy is still a form of order. It would depend on whether they truly believe that they have a "place" in the hierarchy where they belong, or whether they see it just as a means to an end.

Reads pretty close, the old book puts CN as 'lunatics and madmen' in part. I've usually thought of it as society vs individuality / benevolence vs callousness or cruelty.

C/N I've always read in was the person person who doesn't care about the means or the ends, just that the result benefits me or my accomplices

Neutrality is more like doing what it takes to achieve a cosmic state. It places no value on ones self or welfare of others. What you're describing is Chaotic Good.

Chaotic Neutral just means that there are no rules for how to achieve this state. One choice is as good as any other. The more rules, the more Lawful.

C/E would be the sort that is exemplified by the social climbing boot licker

This one might be right depending on how you envision this character. There are certain rules to high society and if their actions are constrained by any of them then they can't be Chaotic. If they only have like... one rule then maybe they're Neutral.