The new 1.5" balls from McMaster-Carr arrived. The stainless steel ball is probably too heavy to really be a good option and with it being so smooth, it doesn't grip your finger too well. The Delrin ball seems like a nice balance of weight and slip. Its surface is smooth but isn't a mirror finish, but it does feel like it will get the job done. The phenolic ball was not round at all, with a molding seam around it and a strange round shape punched into the side of it. It obviously won't work for what I'm needing, unless it was just a fluke. It does have a mirror smooth finish though.
I created a second prototype ball support, incorporating four supporting pins this time. Instead of having nubbins that are left by the milling process, I used a #43 drill bit and taped four screw holes through the model. It seems to have a nice feel for a solid support and the ball rolls better against the steel screws. The viewport at the bottom is too far away this time, once the screws are in to interface with the ball. It measures about 3.5mm from the ball to the underside of the support socket instead of the ~2.5mm that is needed by the optical chip. Better luck next time.
Here is a screenshot from MeshCAM showing the latest design.