I have to do the same thing (minus the wagon- we just carry them) and find that no matter what they will yell and run around fighting the capture. The enclosure we use is an old garden bed that we placed black netting over to keep out predators and birds. They love their daily play time and now spend from morning until evening outside (5weeks old).
We tip the transport box on its side in the enclosure and they will put themselves to "bed" as soon as it gets to bewitching hour and we hear their little bedtime chuckles- we go outside, tip the box over (they know the drill by now), and bring them into the brooder box to sleep. They love adventure time so I think it's worth a little fright in the morning capture for their recess days