If you only have a few pieces of furniture to set, and can set two spikes (literally) in two spots out of the way, you could use different length ropes/cords (that hopefully won't stretch too much). Simply form a triangle with the spike, and the back two corners of the sofa. Then from another spike at another corner of the stage with two other edges of the sofa. There should only be one place that the sofa could go such that the four ropes/cords will be taut. After placing the sofa, move the ropes/cords back to their spike.
Another way would be to form a grid down the back and side of your stage, then you'd have to set the sofa's corner in your notes. (top left corner at 3,4; top right corner at 5,9, etc...)
Sounds like a fun experience. Post some photos with what you come up with.