Yes, symphylans will kill seedlings before they can even put up a stem. There are a couple of things you can try. I've read that they travel along worm tunnels, so digging up the bed helps to get rid of them. Maybe do that selectively because they're not supposed to travel far. I've also trapped them with slices of potato, rutabaga etc left on the surface. Every morning you can turn them over and see/kill what they've collected. Helps you to see how many there are, and where.
If the ones you have are still confined to the soil in bags or containers maybe you could spread that soil thinly on a sheet of ? hot metal in the sunlight. They hate the light and if the sheet gets hot enough it will do them in. Then again there's always the microwave
Initially I thought I was going to have a big infestation - some seeds were failing to emerge and the symphs would be thick on the occasional strawberry where it touched the ground - but I tried a couple of these things and either they worked or I was just overly worried. They haven't been much of a problem after all.