You could try a Displacement Map. Basically you make a grayscale map for warping your image. This would probably be easier to make symmetrical than the Mesh Warp effect.
I do have one question about your project- will most people be viewing the “screens” from the front, or from all sides? In other words, are you sort of trying to create a texture on the objects, or just projecting a video on a weird shape? If it’s not supposed to be a texture, then you may not want to warp your video so that way it will look right from the front.
Nate