Placing an Image into a Photosphere

I have an inverted sphere that has a texture on the inside, and the camera is situated inside the sphere (culling is set to off so that the inside texture isn't culled). The texture is a 360 degree photo. This is a pretty basic setup for a photo sphere AFAIK.

The 360 photo is a photo of a room, and I want the user to be able to place a rectangular piece of art into that room. This rectangular image would need to be warped so that it looks correct in the room (it's okay for the user to provide input on how much warpage to get it to look right in the perspective).

What is the easiest way to do this?

I could try to make a composite image of the art and 360 photo, and then apply the texture, but that seems roundabout. Perhaps I could make a second inverted sphere and apply the art image to that, with the right transparency? Any help would be appreciated.