If you take the nautilus and head to the western side of Saronia (the continent with the castle on it, upper left corner of map, not on the floating continent), there's an area with the most trees on that side. There should be a place between two rivers. If you touch down on the tip of this area that touches the ocean, you can actually dive into it. From there, you can 'bore' into the continent. If you exit into the ocean, it will push you out and you have to dive into the continent again. When tunneling through the continent, you won't encounter any creatures, as far as I can tell.
It is possible to surface at any point within the continent. In fact, you can surface through mountains. Like diving into the continent, entering an area you can normally fly around in will shove you out of the other area and not let you back. With enough skill and dumb luck, you can actually get to Falgabard without the Invincible. Of course, you can't leave after that, but hey, it's still funny.