The cardinal virtues I see being related to the Goddess clan. There's 4 of them.
I don't think it will always be the number 7, we already have 10 commandments. The 4 virtues could be the equivalent of archangels, or the seraphim.
I believe the Goddess clan are the closest to angels yes.
About the demon king, yeah he could be proud hence the bit about Lucifer, but there could be something about him that is "righteous". If he would have people applying the ten commandments then he's more like Yahveh than Satan. As such it could be that the DK isn't really the bad guy, instead it could be the Goddess clan.
Another possibility is that the DK and the commandments represent Christianity, while the Goddess clan are Pagans. The Goddess is a pagan god after all.
So it could be Christinanity vs Paganism, and while there isn't a specific religion in Taizai, there are such themes like the commandments, sins etc.And the period where the Arthurian legends take place in has Christianity spreading, while there are still pagans around, and druids. They would even have rites like Beltaine, so Britannia hasn't being converted completely yet.
So the demon king might not even be a bad guy,he could just be someone who wanted to reform the Goddess clan and broke from them, or he's simply more religious, or even sees himself as a God.
And as far as depicting "angels" as evil goes, it has become a rather popular theme as of late. There's Bayonetta which has angels being the bad guys in the first game(the final boss is god and is a woman

) and even before that the manga Bastard!! had something like that. Although in the end it was more of a battle between Heaven and Hell, with the humans being caught in the middle.
So I guess it's not so strange to have the Goddess clan(which again I see as the closest to angels) be the bad ones.