The integrating cube sounds good if sufficient. You can improve the uniformity and efficiency to arbitrary degrees by adding more surfaces, say starting in the corners, making it k-hedral, approaching a sphere as k goes up, but of course it quickly gets a lot more complicated and tedious. Just doing the eight corners should give a large improvement - beyond that it's diminishing returns, and lots and lots of pieces to deal with. Another option for larger sized ones that's occurred to me over the years, is to put a reasonably-accurate, suitably-sized sphere - like an over-inflated beach ball - inside a cardboard box, and fill the outer volume with polyurethane foam. After it all sets up, you can cut ports and other access to the inside, and roll the liquid coating. You could even slice it in half, and gain full access to the insides, then put the two pieces back together for use. This whole thing would be basically plastic and cardboard, so could melt or burn if you put a very hot source right in a port.
Your flat white paint should be pretty good. It may be worthwhile to see if there's any kind of super-reflective paints or coatings available, like maybe what's used on projection screens, if you want a slight improvement. The coating on my real 12" sphere looks like a flat white TiO2 DAG of some sort. I think when they make these, they pour in the DAG and roll it around to coat the insides, then dump out the excess. Also, as I recall, there's a baffle between the orthogonal ports to block any direct passage. This is more important as the ports get bigger, relative to the sphere size.
Ed
