It may not get a positive reaction on here, and I've only done it once on a bat that was already damaged beyond repair as an experiment, but....
You can bleach the more stubborn stains out using a spray on carpet cleaner foam (Vanish worked for me). Spray it fairly generously all over and rub the foam so it covers all of the bat. Leave it for 24 hours. This will give the willow an anemic white look, so you need to give the whole bat a really thorough sand after this. Once you've sanded it to ensure the bleach is gone, work up the grades as you would normally. Once it's got a nice smooth finish apply a coat of oil all over. The willow will look like willow again and hopefully be all one colour.