Unfortunately, I think it may well be the worms that are doing this. Lumbricus worms such as L. terrestris are not native to the US, they were introduced from Northern Europe. Unlike most other earthworms, Lumbricus worms come to the surface to feed. They will also drag leaves and other plant debris to the mouth of their burrows and allow them to decompose before consumption. Although they are beneficial to the soil, they will occasionally cause damage to young plants and seedlings by uprooting them.

There has been a lot of research done on the effect of introduced earthworms on native forest ecosystems. Below you will see an image which shows the same sugar maple woodland before (top) and after (below) invasion by European earthworms. This image is from a paper published in the journal Biological Invasions (see image for full reference). You can clearly see that the worms alter the structure of the ecosystem on the forest floor and they are capable of uprooting young tree seedlings.

What can you do? The benefits of these worms in your garden greatly outweigh the negative and act as a good indicator as to the health of your soil. Try mulching around the onion sets with layer of grass clippings or leaves to distract the worms from the onions. From your question it seems that you have compost and leaf litter incorporated into your soil, but this likely hasn't been a solution as these worms feed at the surface. A layer of organic mulch on the soil surface will provide a (tasty) physical barrier to the worms and hopefully give your onions respite enough to get their roots established so that the worms can’t pull them up anymore.