Dave, there's no law that requires chicks to be in a container. They would be happier and just as secure if you eliminated the galvanized tub and put the heat lamp in a cozy corner of your coop with lots of bedding, straw or pine shavings, for the chicks to snuggle down into.
You've got no adult chickens to protect the chicks from so there's no reason to stick them in a small tub when they have the whole coop to run around and explore. Just chick-proof it, meaning look for any place a chick can get trapped in cracks of vertical surfaces that might be too close together. Also, block off any cold drafts on at least the north side.
What I would do, though, to make the transition to the coop less stressful, is take the tub and turn it on its side, put bedding in it, and stick the heat lamp so it heats a spot just in front of the tub "cave". Then in a couple days, when the chicks have become accustomed to their new digs, remove the tub. In fact, you could even begin encouraging them to roost by placing them on the perch in a couple more weeks.
As for your sickly chick, have you tried feeding it crumbled tofu with Poultry Nutri-drench sprinkled over it? Or moistened chick feed. Is it not eating? Or is it just a runt? If it's eating and pooping okay, it will eventually catch up.