With mojito, defiantly go for the peat!
Fungicide now would be good, and just keep a close eye on em til it time to wake em up.
You lucked out there!
One cool thing about that tip rot is that when new growth emerges, it will be from several points, each making a plant, the same principal as eye scooping.
A bulb that size I would expect to make 3-5 shoots!
The trade off is that these plants are smaller than they would be if the bulb made only one plant.
Just pot the bulbs like usual, use an extra loose mix if you want to separate each individual plant, I do, colocasias grow so fast that it's more than a fair trade!
So you'll be in the mojito business as long as they make the winter!
