Nuovo Brasil, name-dropped with Cetaganda and Barrayar, seems to be another imperialistic multiplanetary nation. I'll keep an eye out for more name-drops of them. I don't think the Escobaran capital is named; if it is, I don't recall it.

You have a good point about the Betan society = US society. It would even fit with the trend of SF writers having one society be the "default" society they come from, and make the next society be the patriarchal empire.