After finishing the latest podcast, I think I've come up with a decent idea to introduce the Turaga in a way that doesn't make them the leader and/or ruler of their respective region. You mentioned about having a Religion in which there are elemental gods. Well, why not have the Turaga as monk/spiritual types? These would be six beings who have devoted their life to the cause of the gods, and people the Toa could seek spiritual and moral guidance with. They would just be normal village elders, but would be highly attuned to their respective element. To try and use an example, imagine the Toa are like Jedi and the Turaga would be Chirrut Imwe. Someone who can not use the force, but knows it's there and can feel it.
And if you really what to get into it, you could have the leading bodies clash heads with the Turaga about their importance to the island, and have a spiritual and real world division. Maybe because the Toa have taken so long to be "reborn", a lot of Atahka's inhabitants may feel like they had been forsaken or maybe even thought the Toa to be a myth to begin with.
I think this way, you can have the Turaga still fit the same sort of role they did in G1 for the Toa and the Matoran in the wisdom and guidance side of things, but they would have no power or say in what happens over the island.