**Tl;dr ** I made a couch with cushions. The cushions make ambient occlusion on the outside of the couch.
I’ve fiddled with some Lightmass settings but I don’t want to end up abandoning my ambient occlusion to avoid some stupid shadows. The cushions on my couch intersect the inside face by a little bit, but I would think Lightmass would ignore the backface of the outside. The side of the couch is also pretty thin, so setting my Occlusion Distance to a puny amount would make the whole AO thing pretty negligible.