Background plate distortion

I am trying to matchmove a background plate to a miniature set. The shot was looking down a miniature city street, with green screen and reference marks behind. I have a cityscape photo for the background that needs to move with the camera’s pans, tilts and zooms. I used Voodoo to get the camera movement, then in Blender placed a plane with the cityscape photo as its texture behind all the tracking marks. But as the camera moves the background is distorted. When the camera tilts up the background looks like you’re on the ground looking up at a billboard. This happens no matter how far back I put the plane. I did a test in Final Cut Pro where I moved the cityscape image by hand frame by frame against the green screen reference marks and it looked fine. This seems so simple that there must be a way to do it in Blender.

Thanks for any advice

Shouldn’t you parent the plane to the camera?

or set it as the world image texture?

Parenting the plane to the camera resulted in the plane moving with the camera, only the camera zoom could be seen, but not any of the pans or tilts.

When the image is the world texture, the background doesn’t move at all.

Any other ideas would be greatly appreciated. Thanks.