I couldn’t figure out a way to physically arrange the pieces on the board in such a way that the 5th ball was captured without interfering with the rest of the functioning, so I cheated my way into it by putting a gear on top of a crossover to connect two bits that are on two sides of some other paths. It works! (But I figured there must be another way…)
Fun to find so many solutions here that did find an arrangement that works!