I don't know if you've noticed, but the distance between continents only works if the planet is spherical. Ships do go south of all of the other continents and have radar as well as other means of tracking, not to mention accurate sea charts and communication equipment.
Trust me.... if the planet was flat, they'd know about it.
And I may have been off by a thousand, but I wouldn't say it was anymore than that. My last ship had a crew of about 6,000 people. It was the Abraham Lincoln, CVN - 72. My job on carriers was Avionics. I miss those days.