Hi everyone,
thanks again to Gulcan, John & Bjorn.
This may sound pedantic, but: the illusion needs to be perfect, if it be from one angle only.
The room will have objects in background, midground and foreground, so the displacement parallax needs to be held to an absolute minimum. Putting rectangular pictures or furniture in a trapezoidal room won't cut it once this is projected onto a 35ft screen. You will see the mismatch and this will take your attention away from the drama.
This sort of thing was done on Lord of the Rings and Coraline. I can seriously find nothing at all about projection transformations as plug ins for the big commercial platforms like Maya, Cinema 4D or 3D Max. I think the only way to do this is to build a plug in myself. Too bad I'm not smart enough.