36" by any code is not allowed. Are you sure they are stud walls and not dot and dabbed? dot and dab walls will sound hollow as well. I typically shove a screwdriver in the hole and scrape around.

What floor is this on? If it's in the downstairs, then running caving around the room is a good way to hide cables in the void. Or, if you have an attic above the floor you're running it on, you could drill into that space and then run it in there.