Wall cavity is plenty big. It's between 2 floors, sort of, and is a vacant cavity above the furnace area, near the heating ducts. From prior measurements, it should be an exact fit.
Possibility it might stick out a fraction of an inch. If that's the case, I'll just fill it in with some small wood painted black.
My next step is to cut the hole, carefully, there's not a lot of room for error. Then build a shelf for it to rest on. There is good access from the rear side right now. With this finished wood surface, it looks like I need to line the top of the shelf with something that won't scuff it up.