I have corrected exactly this on horsehair stuffed fabric. As suggested Haitian Cotton Cleaner. Unfortunately they no longer do the shampoo variant which would have been perfect. Russ its most likely all cotton construction so indicator dye wouldnt be a major consideration at the pH level of Haitian Cotton Cleaner.
Looking at the spec sheet of Haitian cotton cleaner its a shampoo with a reducing bleach added, might be worth applying Prochem browning prescription, rinsing it through with fabric rinse, the misting spray & go on it.Or even go to the other end of the spectrum & use a Prochem fibre shampoo + fibrebuff + oxibrite application