Do we know the hierarchy of the group, top to bottom?
Nope not really. But the ritual was organized slightly differently than I imagined. The magisters were all distrustful of each other and they are explicitly refered to as "rivals." Originally Corypheus didn't want to involve anyone else. Dumat spoke to him and told him to "open the gates" and receive "power and glory beyond all reckoning." But Cory couldn't do it alone so he went in secret to the Architect so he could come up with a "design" to open the gates. It's unclear what exactly he was asked to build. The term "tower" is used by the acolyte who runs away mid-ritual to warn the Archon:
"If mortals were meant to stand among the Gods
Would they not open the gates for us?
Rather than demand we build a tower,
Blood, bone, and metal to the heavens?"
(Of course "tower" might be metaphorical)
Initially, the Architect refused because he only served "The Grand Plans" and he didn't dare raise a "servant of silence" above him or his god. But afterwards in secret, he consulted Urthemiel who told him:
"Open the gates.
And when you stand before me,
I shall give you designs
That shall rival the greatness of heaven.
I will make you First among the new gods,
And you will build a paradise on earth."
Then the Architect promised Cory "all the skills of Beauty's designs"
The Architect's designs demanded more so Cory had to get help from the other 5 priests. Each of them responded like the Architect. They jealously refused then consulted their god. Each priest got the same message: open the gates and become a god. Then they joined up with Cory and the Architect. No info on their roles but I assume that the Appraiser provided the slaves for the blood ritual.
So it seems that the Magisters Sidereal were an intensely jealous and distrustful group. looks like the only thing that kept them together was the promise that their respective god would make them the most powerful.