""Question ~ how many parishioners can you guarantee for Sunday Mass?"
A good and relevant question it seems to me. Compared to how things were in 1900, Istanbul boasts very few Christians anymore.
When the Roman Emperor gave the "Ecumenical" tag to the Patriarch, he meant that this bishop was imperial, the bishop of the imperial city. That ended in 1453.
The imperial Patriarch is the least these days of all of the Eastern bishops. He's the top dog by custom and by established canon, but only in an honorific sense.
To "rehab" Hagia Sophia as a Christian cathedral is, at this time, an incredible waste of money.
Instead, let's demand that Turkey return all of Cyprus to the Greeks. Better yet, let's demand that all Turks get off the island. And then let's demand the right of Christians to evangelize in Turkey. If we could do that, we could create a situation whereby Hagia Sophia would again at least be useful.
EU admission must necessarily carry with it guarantees that Christians, of all types, may evangelize in Anatolia, not just Istanbul.