Parallax correction when using HDRI environment background

First off: Pony warning. I know some people dislike it when MLP fandom people spread ponies everywhere, but this is the thing I’m working on, so I can’t really avoid it

I’ve been learning to use HDRIs for environment lighting as well as visual backgrounds in Cycles. Wow, I wish I’d known about this earlier! I also managed to learn how to cast shadows that appear to be on the ground with a shadow-catcher and compositing. This works great for still images, but the problem comes when I try to do a turntable animation, because the parallax motion of the environment background obviously doesn’t match up with the part of the model that is meant to be touching the ground.

Example:

This makes sense, since the environment texture is basically a sphere at infinite distance. But is there any way to correct for it, so the character’s foot would appear stationary relative to the “ground” part of the environment texture? I’m not sure if it’s possible, but I don’t have very strong advanced math skills, so I figure it’s at least possible that there is something I’m not aware of involving the texture coordinate mapping, or something to do with the projection.

For reference, this shot was done with my model at the origin, and the camera is orbiting around that point, tracking to a point a bit above the origin. My blend file is too big to upload, but here is my world node setup: