I use an ultrsonic bath( not too powerfull) with a mixture of about 1/4 ammonia, 1/4 liquid black soap, 1/2 ethanol (total about 200 ml) plus 1l hot water.
It works pretty well.
you need to rinse in hot water (two times, for me) and dry rapidly the reeds (on absorbing paper, for instance, vercarefully).