If you look at the my original (unedited) post, you will see that I've spent countless hours researching, experimenting and trying to figure this out.
However, I wasn't using the correct search terms, and only found examples in GLSL. To complicate matters even further, I had to make it specific to HGE, since there is limited support for shaders and other D3D functions without modifying the HGE source.
I also had no knowledge of a linear interpolation function, and even had I known it would've failed to render properly in FX Composer without a proper vertex shader (which would seem pointless for my purposes).
After someone from StackOverflow mentioned a similar answer, I tested it in Visual Studio's Shader Designer and was able to produce the desired output.
I was coming here to confirm that it works, but you beat me to the punch.
In any regard, thanks for the help.