Slitherine

I actually managed to capture the fortress from an AI overwhelmed by myriad threats, including Romanian troops advancing on Istanbul.

I assumed that once I took the place, I could pass naval units and send a battleship to bombard Istanbul.

No can do! Still can't pass the Straits.

You also need to capture the hex north-east of Gallipoli (the other channel hex). Capturing Gallipoli by itself will stop enemy ships passing, but you need to control the length of the channel (2 hexes) to send your own ships through.