@Ben. K. first I would color balance the background to white - the entire image looks off. Upon further inspection there is a lot of artifact noise that could be conflicting with the Background Removal. This was an attempt to use Select Color Range:
In the end, it may be easier to blow out the background to white then use a layer blend mode to multiply this to your existing poster.
I wish I knew how to do what you're suggesting, but I don't.
Our graphics artist is out on sick leave and I'm trying to pinch-hit until she comes back, so this is the only thing I'll be doing in Photoshop and I don't know anything else.