Rendering a literal 3D window frame around the screen, distorted by observer position?

I’m trying to render scenery seen through a window, with the camera position matching the head position of the observer (I have that part).

The scenery is easy, just a distant plane rendered through PerspectiveCamera. But I’m struggling to render the window/picture frame properly.

I want to recreate the effect of walking past a real window, where the depth of the window frame is apparent through the observer moving in different directions (including closer). I guess the glass itself would be stationary, though partially occluded by “wood” unless seen straight-on.

OrthographicCamera seemed reasonable, since it kept the frame the same size. But the frame itself rotates, when I just want it to skew. fiddle with a trivial frame and OrthographicCamera

I’ve also tried a really distant PerspectiveCamera with low FOV and exaggerated lateral movement, which looks vaguely on track. But I’m not sure if I’m on the right track or how I’d relate this to the observer’s position.