This makes the process of deceiving the player much more difficult…
The option with teleporting the player (without any endless level loading) starts to make more sense…
I meant it.
You can replicate the local coordinates of the player relative to his world (the level instance he has loaded), and the second client will use them to set the coordinates for its copy of the other player relative to self world (level instance).
P.S. Horrible things start to creep into my head, like capturing an image of a flat tile of the world and draw it onto a cylinder. 
But I already see problems with collisions (which won’t happen in this case…)