> The question is not about saving someone who I love or care for, but rather some "higher good", which seems to be defined in terms of class hierarchy (dharma vs. mere peasant).

Dharma is not "defined" in class terms, Dharma simply means virtue, righteousness, correct conduct and so no, and "class terms" might be an aspect of it for it. In any case it isn't the only "higher good" around.

> If I die to save someone I care about, that's not because they are better than me, but simply because I care about them.

You recognise that it is possible to care about and care for someone or something other than you, even at your own expense. And it is possible to care other even when they are strangers. We know that because such people do exist.

It is not about others being "better" than you, but a simple recognition that things that are not you also have value (in of themselves, or/and for you). There is nothing more laughable than the narrow egoism of "only I matter".