Sailing for Atlantis (2006)

From the introduction:

This game gets weird. As normal and prosaic as the first island may play out, it's only a matter of time before characters are running around with Cornerstones like Nostalgia, Sword, Happenstance, and Bees. They leave the island called Pillar and proceed on to the island named Apotheosis. In fact, the islands can quickly cease to be physical islands at all.

Also note that the descent into psychedelia is a steepening slope. The stranger your Cornerstones become, the stranger the pages you add to the island, and they inevitably return to your character sheet. By the time you reach Atlantis, it is almost guaranteed to be something very different than you expected, and your character will almost certainly be something that is not entirely human.

Bon Voyage.