IME, H2O2 won't kill most molds... I messed with mushroom cultivation for awhile. It can slow some down, because it kills the spores, but the mold itself survives and will just make more spores. let the soil surface dry out a bit, it'll slow the mold down for sure, and you may be able to transplant the seedlings a few times to isolate them away from it? I don't know if that works for plants, but when cleaning a mushroom culture we transfer to agar, let it grow a bit, transfer away from contams, and repeat until the mold doesn't show up anymore.
***THIS IS JUST A THOUGHT, I HAVEN'T DONE THIS BEFORE***
Take my theory(which is based on working with mushrooms) with a grain of salt and maybe wait for someone more experienced to chime in.
Might be able to do that with something harder for the mold to digest but that'll still hold water for the plant. Coco Coir maybe? I'd probably try switching mediums each transplant(different molds eat different types of material). Maybe Coir, then something like topsoil, and then to peat moss? I'd put H2O2 in with the mediums to prevent any spores on the plant from germinating, and see what happens. My theory is, again, based on mushroom cultivation, not botanical experience.
Might just be best to leave it alone too.
EDIT: Just noticed you've got an Oyster block as your profile pic. Lol so you should know exactly what I'm talking about.