Good point. You'd likely want to also encode something that opaque to who exactly has participated, only really show whether this is the last step and a way for individuals to tell if they have already added their secret.
The really bad part would be that if the poisoner happens to be the last step then the final step would produce the secret before handing it to be poisoned.
The really bad part would be that if the poisoner happens to be the last step then the final step would produce the secret before handing it to be poisoned.