What you say makes sense - actually more sense than what I thought of (with no experience on my side).
My idea was similar - to render out a raw reflection pass at my primary 3d app, then overlay on top of the image and scale it up and down in respect to the position of the image.
Now, I would say I use the raw refl pass, make it transparent where it has to be. The other things, I get what you say, I just have no clue how to pull it off.
Could you explain or show a tut (either video or text with images) in case do not have the time?
EDIT: it doesn’t have to be that physically correct or use shadows. if it moves, it is fine, so it isn’t the obvious static fake reflection 
Now, is it possible to assign mats to images? I thought only 3d objects can have mats.