Warm stratification and mold

I've been pretty successful cold stratifying perennial seeds in the past in ziplock bags in my refrigerator. I soak the seeds, then put them in a ziplock freezer bag with some damp vermiculite and keep them in the refrigerator for the recommended period of time or until they start to sprout.

This is the first year that I've attempted seeds that require a warm stratification period prior to their cold stratification period. I basically used the same method (ziplock + damp vermiculite) but instead of putting them straight into the refrigerator I put them in a warm, dark spot in my house. Unsurprisingly most of them have some amount of mold growing in them.

Should I be worried about the mold? Some seeds would mold when doing cold stratification, but it didn't seem to harm the other seeds. I was planning to rinse the seeds and put them in with some "fresh" vermiculite when I start to cold stratify them in the refrigerator. Some diluted rubbing alcohol or hydrogen peroxide might help kill the mold, but would it harm the seeds?

Is there an indoor method of warm stratification that doesn't promote mold growth? Stratifying them in damp seed starting mix in trays might be better, but that would take up a lot of space.

I use peat instead of vermiculite, I think the peat has some added antimicrobial aspects to it.
Also I make sure that I squeeze the peat almost free of all water before adding it to the bags, you want it moist but not wet.
I like to check them every few days and mix up the baggie to allow for some air to enter the baggie, just by shifting around the peat and seeds a bit.
Like you said, mold can happen. Sometimes it has no effect, sometimes it takes over.
I had pecans pop open with tons of bright blue mold and had no effect on their healthy neighbors, I had Akebia mold out and take the whole baggie.
I wouldn't try the alcohol or peroxide straight up, maybe a very dilute solution, but mostly I'd wash them with water or leave them. It could be your seed just went bad or the mold may even be normal.
Good luck! What kind of seeds are they?

Peat is a good idea. I even have a couple bags but I'm not sure I'll be able to find them under the snow.

Off the top of my head the seeds I have stratifying now are:
Siberian ginseng
Korean pine
Dwarf Siberian pine
Rosa rugosa
Manchurian hazelnut
Beaked hazelnut
Serviceberry (lots of types)
Kristen cherry (not usually propagated by seed, but I'm giving it a shot anyway)
American plum
Canada plum

I think there are a bunch of others, but I'm having a hard time remembering which ones I actually started stratifying and which ones I was just supposed to start. I'm probably too late for a bunch of them now and will have to keep them in cool storage until next year.

I'm trying the "shotgun method" of just planting a lot of different kinds of plants in a lot of different places. Partly because I'm not sure what will do well in my environment, but mostly because I'm a disorganized scatterbrain.