I'm sure others are far more qualified to answer, but on the ones where the mother rhizome was mostly rot but the increases were intact, I took a thin bladed knife and cut between the mother and the increases and then removed the mother being careful go not disturb the increases. I did this with the ones that had viable increases. But the majority of the ones I lost due to rot started under the rhizome so by the time I noticed the rot it was too late to save anything.
Hope this helps.
Blessings