Sky Replacement VFX Warping Issues

I am trying to do a simple sky replacement. I have keyed out the sky and replaced it, but the problem is that it does not match the movement of the camera. I have tried using 2D stabilization, but the replacement sky image seems to warp and doesn’t match the movement of the video. I am going by this tutorial, but it does not seem to work for me. It’s hard to describe the issue, but I don’t know the preferred way of attaching my render.

The video is interesting… and you did a propper tracking ???

I believe so. For 2D stabilization, the track seems fairly simple. Some tutorials show you only need two points, others show a lot of points. I have tried both. I have a low solve error. I do think the problem is with the track/stabilization but I’m not sure where specifically. The camera movements in the video are rather large, and maybe this is cause? What is the proper way to do a sky replacement on footage with significant camera movement?