I've puzzled over this myself and eventually scrapped my attempts because they seemed like more trouble than it was worth, so this is purely theoretical, but... perhaps you can try making a "split screen" effect (first example I could find, might not be the best) in combination with the teleport-wrap that SimoneT describes.
What I'm thinking is use the split screen effect on either end of the level to show what's happening on the opposite end. This way even if the player is e.g. being chased by an enemy and teleports, you can still see a "reflection" of the enemy on the other side, so it looks like a seamless transition. There could still be issues like for example an enemy not reacting to the player when it should because it's just a reflection and not the real thing, but maybe you can make a workaround for the AI or something. Anyway, haven't tried any of this personally but it sounds nice on paper.