I'll try that, I guess even if I am defeated in Anatolia I will always have safe access back home.
Dock your ships. If the stack ottos send looks bigger than you can possibly handle, undock them and block again before they cross. Ship a few guys to somewhere else and watch how the ottomans react. If some move away to react to your siege threat, dock your ships again and let the smaller force cross.
Keep playing games with them until you can wipe their army that way or trap it somewhere. Don't just cross the strait blind and lose WS and manpower to a bad fight.