Egalitarian happy talk about a classless society is fantastical. It only turns the elites into contortion artists denying their privileged place in society, thus discouraging them from exercising their privileges responsibly. See, for example, Paris Hilton.
As for convention, I forget precisely how it fit into Kirk's system and what he had in mind.
Not to read too much into your words about "aspects of a just society," but I do remember that Kirk's aim was for not merely a just society but also a good society, of which justice is but one part. Some conventions cannot be easily justified(heh) upon concerns for justice alone, though such conventions may foster the truly good life. They are basic for a healthy culture.
I brought up the oxymoron of "prudent ideology" earlier. I think the phrases "a just culture" or a "culture of justice" are similarly awkward and nonsensical.
Destroying cultural conventions in the name of justice can rob us as a society of those tiny shared things which bind us together. When it is no longer accepted practice for, say, a man to open a door for a woman, out of some concern for abstract equality, we have lost a small treasure we once held in common. Though these seem like marginal losses, recall that value is often created--or destroyed--on the margins.
For the most part, I agree with you about the loss to society when we turn away from traditions that are the foundation of a culture. But I do believe there is a natural evolution or tendency towards non-fundamental change that is inevitable and healthy in a culture. If this were not the case, we'd still have slavery or women would still lack the right to vote. As for talk of a 'classless' society, I would agree with you that such a thing is neither possible nor even desirable, but class mobility is a necessity, in my opinion, in a society dependent on Natural Law and Judeo-Christian ethics. If I understand Kirk correctly, his view on Class was more along the lines that those lines were drawn more along hereditary lines...which is NOT what this country stands for.