This may not be easy in AE, but one thing I would throw into the mix on top of transfer modes is a Displacement Map. Use the fog layer (or, better, a copy of it) to drive the displacement, so the projected movie will get slightly distorted by the fog – as it should. You may need to tweak the levels of both the fog and the movie, and it may be better to make the visible background fog less contrasty than the fog used for displacement (this is why it’s better to duplicate the fog layer). I think you should be able to get a decent result this way.
Another useful addition might be a volumic light representing the projector beam. Trapcode Lux may be useful here.
By the way, this may not necessarily be easy even in a 3D app, unless you have a dedicated plugin for making 3D fog and are comfortable with texturing, lighting, volumic lights etc.
Hope this helps,
AA