I agree, you should try to remove the mushy stuff to prevent it spreading and to help the rhizome dry out. I got quite good at that this summer with an entire delivery of rhizomes that were wrongly treated in transit. Depending on how bad the rot was, I used a finger, a spoon, or a knife to get rid of the mush, then planted them in the sun. A couple had what I thought of as radical surgery, where I cut off more than a third of the rhizome. Almost all are recovering, some more quickly than others.
