Notes from a company that makes plastic spheres
I just spoke with these guys-
They make plastic hemispheres using "freeform vacuum molding". There is a price list for hemispheres on the web site- $169.30 for a 3/16" thick, 3 foot diameter acrylic hemisphere, making $338 per sphere. Polycarbonate (lexan) would be way better for this application, but costs 2.5 as much- i.e., $845 for the same size sphere. Unfortunately, this company can't make true polycarbonate hemispheres- they end up a little shallow, so we'd have squished looking balls, which I think this could cause trouble for the motion.
We could also look into replicating this process ourselves. It shouldn't require a massive capital investment like injection molding, but it would still have to be pretty cheap to justify making them ourselves out of plastic. There may be other processes for plastic that make more sense for diy, like fabricating strips or sectors and bonding them. and of course, metal is definitely an option, in rod, sheet, or other form.