So, I hope this is the solution, Jamie.
Thanks for the file, I think I see the problem, correct me if I don’t!
The alpha that you have used works, but only for the projected area.
Edit, while you wrote I prepared the file, so the idea what’s going on is perhaps already clear :O) /edit
Since the projection camera is in front of the render camera, the image and with that the alpha is smaller. I placed a Plane there to explore the situation for a moment, the plane is not needed, but it helps to get clear about the problem, see image)
What you need to do is, set left sided from the material, a new additional material, set to Color black, and Alpha completely to transparent. No other channel on, even the Color could be off. However set this material in the texture Tag to tile. Leave your projection as it is, it is OK, so far I understand your target.
This will take the gray frame around the image away.
I can attach the file here if you like, or if you need it. Let me know.
My best wishes