It sounds very difficult to do something that will allways look ‘right’ or how maybe you imagined it.
To further explore your concept why don’t you use a Decal instead?
That would be very similar in that it would be a projection onto a surface with a transform. You can then easily move it around by hand to interactively see how it behaves.
I don’t think you could do something that allways wrapped around various corners correctly etc.
I think you have to decide first conceptually how you want it to ‘project’ on your various walls in all the different situations you can have and then try to figure out if that is possible.