I think it’s definitely an ambitious dream! At the present time, the virtual fitting rooms are professional products sold to corporate clients. I’m not aware of anyone making a hobbyist version of the software to place images on top of reflections. I believe the closest thing we have around here to a commercial devices is one guy made a photo booth and he did a lot of the coding himself.
Don’t get discouraged! It’s not an impossible dream. Just understand that there are challenges. Around here, we can definitely help you with construction tips, parts sourcing and test & tuning. And you might find a genius looking for a challenge.