Cory.. I'm not sure of your weather conditions there but normally soft rot comes from plants being in wet humid conditions and unlikely it would attack your whole garden at once especially during the cold months unless you completely buried them or mixed in some sort of fertilizer but even then you most likely wouldn't see that until the temps warm up and ground temp hits a certain point.
The plants I have issues with are the same way they don't show the grey mold on them and there not spongey but more soft to the touch there is a difference so to say because Ive had both but Botyrtis attacks in different forms and the secondary part of it is the bulb will rot and this is what your seeing. I took a pocket knife and cut out the center of the rotten bulbs it will allow air circulation if you do this you should be able to save the increase unless it's spread to it.
I let what survived stay and then I moved them in late summer, pay attention to the bulbs when you dig them and look for a dark brown color in the bulb it will still be attached to what you are trying to save make sure you cut that out it is the botyrtis and I think it stays with the plant and attacks over winter when the plant is stressed and the conditions are right if left in place. The ones that are not mush now but the top comes off in your hand will turn to mush when the spring rains come remove those now as well or cut a slot in them. I left a few last year that I thought might be ok because they showed a small leaf like the bulb was trying to recover but within a month they were gone and the increase as well so better to remove the rotten bulb it will never bloom. Hope this helps I'm hoping ISU can come up with something that is a preventive for me to use going into the fall and winter months but won't know for a while.
Good Luck send me a list of what's lost I may be able to help
