I have seen many scenes in which the camera start as a POV then the character enters the frame in the last minute and the shot stops being subjective. I believe that’s in many Scorsese movies.
If your director likes this kind of solution you can avoid doing all the complex, more expensive, green-screen work that replace the mirrored image will suppose.
Sorry no direct answer to your question, maybe other COWer has an easy technical solution. But I love the POV-to-character kind of shots, anyway.
I hope this helps