I'm now aware that the soil was a bad idea and may have caused damping-off. Any other ideas?

I think soil would be the largest potential culprit. Not sure about others, but here's what I would do. Buy a good quality potting mix, I love Fafard products, but there are lots of good ones. Clip the cotyledons and re-plant the seedling deep. Only water when the mix is dry and the plant starts to wilt just a little bit. You should see the leaves droop pretty soon after the soil goes dry. Also seedlings don't need as much nutrition and adding full strength fertilizer is not beneficial yet. If you fertilize only use fish emulsion at 1/2 or 1/4 strength.

I agree a lot with that. If you want to use materials that are guaranteed to have hordes of fungi in them, like compost and outdoor dirt, at least sterilize it first (dampness and lots of heat). Dirt isn't an automatic seedling killer; after all people plant seeds directly in the ground, but when you have problems it's often helpful to cut back on the possible suspects, and (in its own way) indoor sprouting can be very hostile to seedlings.

I use hydrogen peroxide mixed in water in a spray bottle to spray the soil - it seems to kill the damping off disease.

won't work if damping off already active

No sure won't. I thought I mentioned that but musta been another thread.

It is a good idea to always use a spray bottle when starting seeds. Just remember to also mix in some peroxide.