The "professionals" never seem to get anything done.
They can't see the forest for the trees.
Christians were able to run "the place" for almost 1300 years. You are obviously unaware fo the history of the region.
As I said in my earlier post, I or someone else will find out more details and get back to you.
The ususal method is to have a pastor or bishop in charge of it, with sufficient staff of some sort to ensure the maintenance of the physical plant and the scheduling of Liturgies etc. Simply throwing open the doors and inviting one and all, willy-nilly, is a recipe for chaos. It's also NOT what Christians have been doing for the last 2000 years.
If that's all you have, I'm for leaving the Turkish guvvies in charge until the Christians come up with a plan.