It's OK to leave the plant out of the ground for an extensive time. Let it dry, but remove it from the fan on Monday - you don't want to overdo it. These days I just put the plant on a small, dry towel for a day. Don't plant until you know that you have removed all of the rot. Leave the remaining offsets on the mother. Put the mother and offsets where they will get really bright light, but avoid direct hot sun. A week after you are sure the rot is not progressing and is gone, start misting the plant once a day and wait a couple of weeks to make sure the rot is gone. The offsets attached to the mother should still grow. OK to plant once you are sure the rot is gone, but that delay should be at least a week to be sure.
The offsets separated from the mother plant can still survive. I don't know how big they are, but if very small (1/4"?) they will be much more susceptible to drying out. Plant remaining stolon in dirt (I'd use a pot for now) and be sure to give enough water so they don't dry out. I'd start off with normal dirt without a lot of water in it, mist the surface well, then enclose in a plastic bag and seal it. Check daily to adjust conditions if necessary. Bright light, no sun, especially when in the bag.
