Anyway. The existential dread.
William the actor never existed. The jump is Generic Worm Fanfiction, but your Jumper system had a little accident. It found a shard and, under the directions of a random doG, fused with it, resulting in catastrophic errors. Originally, the jumper system was supposed to insert random Joe#234999943 into the fanfiction of their choice. Instead, the system fused with William Manton's Shard. Original Joe was an actor, and being Manton's shard means that Manton's the one who's going to be the Jumper now. The mashup resulted in a new William, one who remembered an entirely different life that never existed. He is an actor like Joe was. His name is William, and he played Dr Manton. His coworkers are all alternate versions of real people from Manton's life. He remembers media from Joe's life, though altered to fit with his new memories.
The death islands are the result of the Shard's desire for conflict and the Jumper system's habit of importing people to new settings.
The missing time is because the fusion actually happened two months or so into the jump. Before that, Joe was living his new life as a Jumper in a worm fanfiction, completely unaware of the looming disaster.