Did you post a link to the wrong photo? The deceased plant pictured was not grown to four or six leaves.

How can you opine about "root damage"? The roots are hidden by the Jiffy pellet bag. Surely you did not plant it out without removing the netting?

Just looks like this plant died from "damping off" inside, and was nowhere near ready for transplanting outside, and obviously not "hardened off" for transplant outside.

The pictured plant has four leaves. They are just shriveled because the plant is dead. I don't think it's root damage, precisely because it was planted pellet and all, and because you can see that there's about an inch of healthy stem above the surface of the pellet.

These plants look fine up until the point they are transported outside. I don't think they need much hardening beyond letting them grow four to six leaves. Our temps are around 75 daytime / 55 nighttime.

Symptoms do appear to be consistent with pythium damping off. I'll soak the soil in affected areas with fungicide before trying to replant.

I'm not sure from your after the fact photo exactly what is going on, but you need to understand hardening off is much more important than placing the plants outside in similar temperatures. There is no indoor lighting that comes even close to the real rays of the sun, and equally important is wind. You've had the seedlings in a carefully controlled weaker light, windless environment....they must have a gradual acclimation to the hostile-to-pampered-leaves outdoors or they die.

They are started on the windowsill, so they get direct sunlight a few hours a day, and I keep them outdoors for at least a week before planting. I've even started using planting sleeves because it's almost July, and I'm at 33 north, so there seems to be just too much sunlight for many of my veggies. I just don't want to keep them in those pellet bags for too long, because they are too small and there's not enough room for the roots.

Like I said, the damping off (fungus) keyword seems to be on the mark.

You need to harden them off properly before planting them out. Modern windows block UV light. That might be damping off, but you should be able to see the fungus inside before planting out. Whenever I get it the seedlings keel over at the soil surface, not some way up the stem.

Dan