Take a beach ball or large balloon the size you want, construct a stiff wire frame around it and deflate it and pull it out. Insert the ends of the wire frame between the nail-on plate and the wood and screw it down tight. Just bear in mind the temperature of a 150 watt or higher bulb might brown your material if the ball is too small. Test it in the garage for a few hours to make sure it won't embarrass you when you whip it out in public. Make a bunch of them and tell production they have to rent them for enough money to make back what they screwed you out of your rate.
Every tool has it's application.
Recently I was put in a situation where I had to light seven woman in various different settings, around a table, in a living room, in a den etc. The catch is three cameras had to roll on them in opposing directions simultaneously, and two had to be on moving dollies. In other words, light 360 without seeing a stand, and have virtually shadowless lighting, so there was a place for the two overhead mic booms to float without casting a shadow. The dialogue was all spontaneous, so the cameras had to be prepared to be on any one person, at any given time without shooting the camera in the opposing direction. I don't know how, but somehow it worked.