Welcome, Wayfarer! I'm a convert to the Coptic church, and had a long, slow road myself, through Baptist, charismatic and Anglican churches.
Admittedly, I am at a point where I am standing in the shallows on the west side of the Bosphorus - in just about ankle deep. An Orthodox friend has repeatedly told me that I am orthodox and just don't know it yet - maybe.
What an interesting image! As I was pondering conversion to Catholicism or Orthodoxy, I kept picturing myself as standing outside these beautiful churches and peering in, getting a whiff of incense or a waft of singing, but afraid to step through the door. At that point I wasn't even in a Protestant church anymore, so I really was out on the doorstep.
Although, having lived in Istanbul, I'll tell you- standing even ankle deep in the real Bosphorus is no place to be.