Endless White Room
I think the way to render an infinite room is actually a cheat. Normally what you would do is render your character without any environment(floors,wall,etc.) and in a composting package like after effects or something similar put the character over a white background. What you call "contractors white" sounds like ambient occlusion. You can render the character and ground with ambient occlusion which you multiply over your beauty render in the composting package. This gives the illusion that the character is in an infinity room. I am sure it is to do with ambient occlusion
I kind of have an idea but cant get it rigged properly
Conquering The World One Pixel At A Time !!!!