Likely you are experiencing nocturnal diners. Some of the usual suspects are caterpillars (cutworm, army worm), weevils and even earwigs are known to eat tender youth foliage. The 60-90% would seem to preclude inclusion of an animal; likely to clean up a find.

Try a few traps spread along the plantings. One effective night trap is a shallow tin or small pie plate with a couple tablespoons of vegetable oil and a teaspoon of soy sauce. I have employed them with success, even for cutworms. The soy attracts them and the oil more or less drowns them. For the earwigs, a damp roll of newspaper or a 12-15" inch of old garden hose gives them a daylight refuge that can be collected or emptied at dawn into a soapy water.

A garlic spray may deter some. You might even try a thin blanket of chopped straw mulch which while retaining moisture also limits the maneuverability of the pests at the base of the young leaves. The mulch also seems to encourage more predators like spiders.

Otherwise, it is a matter of timing to get the carrots in while cool before the appearance of the pests. Even then I often leave a row cover over the seedlings; they will grow upright as they mature and you can lift the cover after signs of good growth.

Good luck.

Probably earwigs. Caterpillars first came to mind but without the seedlings there was nothing else nearby for them to live on. But I have seen plenty of earwigs around but they never seemed to do any harm so I always them alone. I have also had amaryllis seedlings yanked out of the soil and lying on their sides with a part of the leaf chewed up. I suspected birds but it happened even after I put the pots where birds couldn't get to them. I guess earwigs can easily pull those out with their pincers. Now I'll go after them the same way I go after slugs.

I don't think earwigs would pull out your amaryllis seedlings. That may have been birds thinking it was a worm. They do that to our onion sets just after they are planted. Earwigs would just eat the tops.

The carrots sure sounds like earwigs had a feast. I have had a problem with earwigs this year. I planted a bunch of marigolds in a bed and in 1 night they stripped them down to skeletons. I found this recipe on this site and it works like a charm. I set it out 1 night in a baby food jar with a little over 1/4 inch of bait and checked it the next day. It was full of baby earwigs. It catches the adults too but later.

Bait for Earwigs.
Equal parts of soy sauce, oil and (molasses or corn syrup). The molasses or syrup is bait to attract them--the oil doesn't allow them to crawl back out and the salt in the soy sauce finishes them off. Put it in a small container(small yogurt container, larger pill bottle, specimen bottle or anything that is fairly deep) covering 1/3 of the bottom with the mixture and bury it up to the brim in the soil. I like the smaller ones because it doesnÂt take as much bait and they are easier to bury into the soil, But my neighbor uses margarine containers. Prop a lid over it so it doesn't get diluted by rain and so it is a nice dark place for them to hide--ha. When you prop the lid, leave a small space for them to crawl into the container. You might have to wait a couple of days for it to work, but mine were full of them the next day. It does work. Your container will be full of them.

Now organicdan says that just soy sauce and oil works too. It might be worth an experiment to see which works best.