Comet Cleanser has bleach in it -- and yes you sprinkle it on the rotted area. I would guess that rain will take the product down into the rhizome, and kill the rot.
I've never done this before -- have only heard about it -- so don't know how successful it'll be. I know that we're headed for more soaking rains here -- as though we've not had enough -- so trying to dig these out and replant is an exercise in futility. And I'm not willing to spend the time to pot them up -- too much other work to do.
