OK, I tried out the full Cycles method and got it to work . . . soft of. It turns out, the only way I can get it to cover the whole front face was to plug the ImageTexture into the TextureCoordinate's Window node. The others either look like warped versions of my test texture, or the texture only covered the bottom half, with the top and some of the bottom solid black. That's why I started experimenting with the other TextureCoordinate nodes to see if I could cover it all.
The problem now is, it's twice the size it should be, so how do I get it to display as I originally had it? You can see the difference, as the backfacing texture is still the original Image_Map setup.