Here's an out-of-the-box idea. Instead of expensive conveyor belts, use high-quality commercial sanding belts. They are cheap, readily available, and can easily handle the heat and load of the little foam balls. The commercial-grade belts have a fabric backing, and if you use a fine grit belt (like 150 or 220) you get a high-friction surface that still grips when dirty, and will not damage the balls. I've tested a launcher built from two belt sanders and the balls didn't show any particular damage.
Other advantages are that sanding belts are light weight, available in a wide range of sizes from 18" in total length -- which means about 9" if you lay them flat -- to 93-1/2" in widths from 1" to 4" for common sizes, and up to 36" widths in some commercial applications. Did I mention that they are relatively cheap?
Some of the students on our team were worried about their durability. Trust me -- your foam balls aren't going to be as much strain as a 20-pound piece of rock maple.
I usually buy mine at
Klingspor's shop.