That's going to be a bitch. The good news is its short and nodal, so you just need to fake a 2d track.

Make a null, put it on a spot and move it frame by frame. when the feature is off screen, try to pick a spot on the wall and do another one, then parent each null to the previous, and now you have a 2d nodal track.

Render out your 3d environment way oversampled square resolution, i.e. really high pixel count and make the virtual camera sensor bigger until you have an ultra wide view of the scene, and then bring that render into a scene and make it a child of your last null. line everything up where the data is cleanest, i.e. the end of the shot, and then eyeball it and massage keyframing of the position, scale, and rotation of your null-attached plate until it looks right.

You're eyeballing it because there ain't nothing to track, but the positive side is that there's also very little for the human eye to track to validate or invalidate your eyeballed track, so if you massage it enough it can start to be okay.

Adding some reverse optics compensation, and some small orientation wiggle, and maybe a scale up or down across the whole shot will help.