I'm sure this isn't the best way about this, but extending the class doesn't allow access to the class's private members (properties and functions!) which made overriding the GLSL difficult or impossible. So, I took the entire WebGLTile file, copied it and put it with my own code. I had to alter all relative path imports from . to ol/ but it worked.
I was able to change the GLSL in the private parseStyle method/function. While this achieves my goal, I realize that copying this class will likely cause compatibility issues in the future. If there is a better way to do this by extending the class, I'm still open to any and all suggestions. Thanks!!!