[Gogar]

is the ceiling hollow between the projector and the fixture? is it possible to punch a little hole right behind the projector and fish it into the side of the ceiling box? The ceiling box should have a knockout in the side and you could fish through there. Unless there's a stud or something in the way between the two.

I would set the ceiling fixture to 'always on' and do a Hue light and a hue switch on the wall or something like you suggest. Or whatever brand of wireless stuff you want to use.