Hi April,
I would not keep moist mulch in there. It could cause upper respiratory infection, mold or various staph, bacteria infections to start showing on the skin. He needs hot and dry conditions, but in the wild, even in hot desert areas they might wake up with a dew on them to which they'd lick and hydrate themselves to prepare them for the hot day.
In captivity we'd replicate that by misting with warm water, in the morning. I find heating them up an hour first before misting, get's them to lick the mist more than if misted when cool. You'll find that if you put hot water in a bottle, and mist your wrist, it's just warm, so I use hot water.
And after they've licked the mist a bit, you can start them on calcium drops by placing a drop a day on the nose while licking mist. Not force feeding. With their being wc they've been under a great deal of stress, and you want to eliminate that stress as much as possible.
If that's a wood enclosure and only visible from the front, that's a step in the right direction. You want to fix the set up and then leave it alone. Everytime you move something, you create stress and interupt aclimating.
Chances are they have parasites being wc. In the wild they can survive with these parasites but being stressed thru captivy and loss of appetite has weakened their immune system, causing parasites to gain a foothold on positive gut flora.
I'd suggest buying something that produces positive gutflora or beneficial bacteria. Like Benabac. Not sure if it's still available but they had a orange paste that the lizards actually like. Many species of lizards love the orange colored foods.
Even if you bought plain yogurt with a label that says it has beneficial bacteria or cultures? Using a dropper after misting to get them licking you could put a few drops of it on his tongue. The main thing is to get him hydrated. And if that works you can do the fun stuff like bug flurries. Mash a few crickets in, add a few peas or carrots, and vitamins. Yummy!
To start him out on the new regime, you could take him out early in the day, and soak him for 10 minutes in shoulder high warm water, being careful not to leave him alone. Dry him well, and leave his current temps as they sound good. (I don't remember your night time temps, but until he's fattened up, I'd keep a night light on to about 75 degrees to keep his tolerances high.) After that bath, I wouldn't take him out again. Put a few plants infront of the cage to block his view and create more privacy.
Concerning waterbowls, I'd just have 1, and in the center of the cage. They can not see water so everyday after an hour of light, put in the empty bowl and after misting their faces, slowly pour water into their bowl. If I thought you had a space on top of the cage, I'd say put a plastic cup full of water, with a pin hole in the bottom, on top, above the waterbowl, so it slowly drips into the bowl. And they can then see the water and it attracts them.
You might also try a jar lid and dropping in a few wax worms and see if that interests them. After hydrating a week you might want to look into getting a vet check on fecals for parasites. That can be dehydrating and can kill positive gut flora as well, so you'll want to keep up with the daily misting and fluries, till you see fatpads on head. If tail is totally sunken in, it may be too late, but you'd be amazed sometime how long they can survive.
Good luck!