Are his urates snowy white, or yellow/brown. Iguana poop comes in thee parts; the brown or dark colored feces, and the white soft urates, plus clear fluid.
It's not bad for him to eat at night or evenings. We have to assume he may still have some Relocation Stress. Many such iguanas eat at night, in private, when the new sights and sounds are dark and quiet so they can relax.
The only problem is that he still associates eating by you offering food by hand. But, holding a dish piled high with good veggies/greens is far, far better than him only accepting one bit of food from you at a time. The "food piled high" is important. He should have his morning meal presented to him every day whether he eats it or not. Someday he will surprise you and clean that plate.
Is he still accepting food only when you offer it? Do you give him large fragrant servings in the AM and again in the PM? Those offerings have to be very consistent, even if you end up holding a plate of food up to his snout in the end.
I'm concerned he's not eating enough despite your efforts. And he's still a weak climber.
All this to lead up to asking if you may consider taking him to an exotics vet or a dog-and-cat vet who's trained himself to treat reptiles. Your green guy may have a stomach ache or just feel sick, caused by gut parasites or gram-negative bacteria.
You can bring the vet a fresh fecal sample, the size of an almond and the vet will do a blood test to check his metabolism. This often brings miraculous cures and renewed vitality.
The consequence of treating with antibiotics is the friendly and necessary gut bacteria are killed off. So after treatment, you need to feed him probiotics twice a day for a week or so. Avian vets generally have probiotics balanced for birds, which are good for iguanas. I've only used human grade probiotics that are known to be dependable. The vitamin and supplements zone in your local organic food store will have these. Pick one that has the most different types of flora listed on the label.
In case his gut is unhealthy, you can start the probiotics right now, on your own. Give him a little bit per probiotic serving. Use a three cc plastic syringe (from your pharmacy - no needle on these) to suck up some one cc of probiotics, open his mouth, and dribble it in at the back of his jaws.
For igs who wouldn't open their mouths no matter what, and the struggle to force it open was too stressful, I parted the iguana's lips near the back of its' jaw, pressed the syringe tip against it's clenched teeth, and slowly squeezed the contents through whatever gaps are in the dental system. That actually worked for me with extremely stubborn or scared igs.
You can use a tongue depressor to press against the teeth at the tip of his snout, and move it in a prying motion until he bites the stick. At that point his jaws are parted and giving the medicine is easy if you can do it before he figures out how to spit the depressor out.
Pulling down on the dewlap is used as a last resort. Pull firmly and steadily on the front end of the dewlap until the jaw muscles tire out, and the mouth opens. Roll him up in a beach towel or a blanket so only his head is sticking out. That gives you the use of both your hands to do the job. He may be very cooperative, or he may resist with all his strength.