Sounds like a fungus. You could try 4 teaspoons of baking sods in a gallon of water, which will kill it. However, test it in an unobvious spot first to make sure your new grass is going to deal with it.

It sounds like the inch-deep grounds are the source of the issue--continuously damp, rotting away like mad, and hosting countless bacteria and fungi. No matter, it's fixable.

If you could shift your watering so the new grass blades don't go wet overnight that would certainly help. The suggestion I saw for a new seed bed is to water three times daily for ten minutes at 10 AM, 2 PM, and 4 PM.

Once the grass sprouts (like yours) you should be able to pull back to once a day. If you could do that in the early morning hours, that would be perfect.