After my last post I got to thinking and came up with a really hacky way to do this, I basically just spherified a cube, chopped it up into 5 sides, and assigned a render target to each one. Then I attached it to the player camera (so the camera is basically just looking at a spherified cube with a bunch of render targets on it). Worked better than expected.
You can get away with as few as 3 render targets if you don’t need the distortion to be particularly intense.