I did actually crack it. With the help of AlanT in the other thread, I was able to get the UVwarp modifier to move the texture in sync with the camera. This allows me to move the texture around the warped area in the plane:
It’s not perfect, but I can manually keyframe the camera to move the texture over the warped parts of the plane and still use shapekeys to control the intensity of the warp. This works, but I’m still open to hearing about better ways of doing this.