Hi @canadianrenegade nice post!
In order to do a proper and simple stratification you need: sand, one tablespoon of crushed mangal charcoal (barbecue charcoal), and tap water (with chlorine).
The charcoal prevents fungus from colonizing the seeds.
But do not apply the charcoal on the sprouted seeds, it will inhibit their growth.
About the fungus that attack your buckeye seeds, it looks like the fungus that decomposes the dead wood in the forest.
The mycorrhizal fungi that is put in the potting mix is made of a number of different species of fungus, not all of the species will survive and prosper in all conditions, and probably the manufacturer used humus made of leaf mold from the forest in there mixes.
The fungus family is big and different ones have different purposes, some eat the dead wood, some are parasites while others live in a symbiotic relationship.
You could put the cups with the sprouted seeds next to the window and they will grow as big as the amount of sunlight they will have.
After a while if the root started to grow and it is to cold for the top part to grow, the root will rot.
I hope i was helpful.
I wish you a nice day.