Uv mapping / 2D world wrap around

Hey, We are two students who is doing a project to make a 2.5D game with the oculus rift and UE4.
We want to wrap the 2D world around the player, but want the game to stay in 2D logic(as enemies and the player use 2D pathing, and 2D physics etc).
So we discussed with our teacher about maybe using UV-mapping of the 2D world to project it on a cylinder.

The problem is that we are pretty lost on how to attack this problem, is something like this easily achievable with the current engine tools?
We would appreciate any suggestion/guidance to help us get closer to solve this.

If anyone have other solutions/approaches to the problem we would love to hear those.