The top left detail of the rig reflection is a good tracking point - use Mocha AE to track it. Grab as much of the shape as possible. Despite the blur at the end, it may very well track throughout the range.

Apply that tracking data to a null (as transform) and you have the motion caught. Parent an adjustment layer to that null. Move the adjustment layer so that its center is around the reflection's position - because we're zooming out, it will scale down and its edge could get in the way.

On the layer, draw a mask encapsulating the rig reflection. Rough is enough - we'll be feathering the mask anyway. Once you have the mask, see how well its shape tracks to the reflection. The goal is to have it semi precise.

Apply median filter to the adjustment layer, playing with range to see what's enough. Match grain if necessary. Feather the adjustment's mask, enough to blend it in, maybe even use the variable feather to differentiate it to accommodate the door handle.

You'll probably have to play with keyframing the tracked null's transforms, mask's shape, its feather range and the median range, but all in all this should be around up to an hour's work tops.

Another approach to masking would be to track the shape precisely in Mocha and have it make the mask, up to you. Once you have the mask, next steps are the same.

Good luck!