I'd suggest adding a small bowl of water and taking out the towel. I can't remember why right now for the life of me, but there is a reason that you don't really want to make contact with the eggs and water like that. If your temp is right, the water level can be adjusted to produce the right humidity. Do take into consideration that the hay might also absorb some of the heat from your lamp.
Perhaps you could have your cooler, layer the bottom in hardware cloth (the thin metal grid wire), and lay the eggs in with the bowl of water at the center (arrange the eggs around as evenly as possible)? The hardware cloth should give them some stability (so they don't roll when you try to turn them, but wouldn't absorb so much heat as the hay. It will also give them something to stand on once they hatch. You can even layer a bit of cheesecloth over that for added traction and ease of clean-up. If you have a weather-station style thermometer with humidity reading, you can leave the probe inside, but know what's going on it there without opening the lid. Just add a little bit of water or remove it to adjust.
Perhaps you could have your cooler, layer the bottom in hardware cloth (the thin metal grid wire), and lay the eggs in with the bowl of water at the center (arrange the eggs around as evenly as possible)? The hardware cloth should give them some stability (so they don't roll when you try to turn them, but wouldn't absorb so much heat as the hay. It will also give them something to stand on once they hatch. You can even layer a bit of cheesecloth over that for added traction and ease of clean-up. If you have a weather-station style thermometer with humidity reading, you can leave the probe inside, but know what's going on it there without opening the lid. Just add a little bit of water or remove it to adjust.
